Pre-Algebra Examples

$(\frac{6}{5} x^{2} - 2 x - \frac{3}{5}) (\frac{6}{5} x^{2} - \frac{2}{5} x + \frac{3}{4})$

Step 1

Simplify terms.

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Step 1.1

Combine $\frac{6}{5}$ and $x^{2}$ .

$(\frac{6 x^{2}}{5} - 2 x - \frac{3}{5}) (\frac{6}{5} x^{2} - \frac{2}{5} x + \frac{3}{4})$

Step 1.2

Simplify each term.

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Step 1.2.1

Combine $\frac{6}{5}$ and $x^{2}$ .

$(\frac{6 x^{2}}{5} - 2 x - \frac{3}{5}) (\frac{6 x^{2}}{5} - \frac{2}{5} x + \frac{3}{4})$

Step 1.2.2

Combine $x$ and $\frac{2}{5}$ .

$(\frac{6 x^{2}}{5} - 2 x - \frac{3}{5}) (\frac{6 x^{2}}{5} - \frac{x \cdot 2}{5} + \frac{3}{4})$

Step 1.2.3

Move $2$ to the left of $x$ .

$(\frac{6 x^{2}}{5} - 2 x - \frac{3}{5}) (\frac{6 x^{2}}{5} - \frac{2 x}{5} + \frac{3}{4})$

Step 2

Expand $(\frac{6 x^{2}}{5} - 2 x - \frac{3}{5}) (\frac{6 x^{2}}{5} - \frac{2 x}{5} + \frac{3}{4})$ by multiplying each term in the first expression by each term in the second expression.

$\frac{6 x^{2}}{5} \cdot \frac{6 x^{2}}{5} + \frac{6 x^{2}}{5} (- \frac{2 x}{5}) + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3

Simplify each term.

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Step 3.1

Combine.

$\frac{6 x^{2} (6 x^{2})}{5 \cdot 5} + \frac{6 x^{2}}{5} (- \frac{2 x}{5}) + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.2

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 3.2.1

Move $x^{2}$ .

$\frac{6 (x^{2} x^{2}) \cdot 6}{5 \cdot 5} + \frac{6 x^{2}}{5} (- \frac{2 x}{5}) + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6 x^{2 + 2} \cdot 6}{5 \cdot 5} + \frac{6 x^{2}}{5} (- \frac{2 x}{5}) + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.2.3

Add $2$ and $2$ .

$\frac{6 x^{4} \cdot 6}{5 \cdot 5} + \frac{6 x^{2}}{5} (- \frac{2 x}{5}) + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.3

Multiply $6$ by $6$ .

$\frac{36 x^{4}}{5 \cdot 5} + \frac{6 x^{2}}{5} (- \frac{2 x}{5}) + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.4

Multiply $5$ by $5$ .

$\frac{36 x^{4}}{25} + \frac{6 x^{2}}{5} (- \frac{2 x}{5}) + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.5

Rewrite using the commutative property of multiplication.

$\frac{36 x^{4}}{25} - \frac{6 x^{2}}{5} \cdot \frac{2 x}{5} + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.6

Multiply $- \frac{6 x^{2}}{5} \cdot \frac{2 x}{5}$ .

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Step 3.6.1

Multiply $\frac{2 x}{5}$ by $\frac{6 x^{2}}{5}$ .

$\frac{36 x^{4}}{25} - \frac{2 x (6 x^{2})}{5 \cdot 5} + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.6.2

Multiply $6$ by $2$ .

$\frac{36 x^{4}}{25} - \frac{12 x \cdot x^{2}}{5 \cdot 5} + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.6.3

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 3.6.3.1

Move $x^{2}$ .

$\frac{36 x^{4}}{25} - \frac{12 (x^{2} x)}{5 \cdot 5} + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.6.3.2

Multiply $x^{2}$ by $x$ .

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Step 3.6.3.2.1

Raise $x$ to the power of $1$ .

$\frac{36 x^{4}}{25} - \frac{12 (x^{2} x^{1})}{5 \cdot 5} + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.6.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{36 x^{4}}{25} - \frac{12 x^{2 + 1}}{5 \cdot 5} + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.6.3.3

Add $2$ and $1$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{5 \cdot 5} + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.6.4

Multiply $5$ by $5$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{6 x^{2}}{5} \cdot \frac{3}{4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.7

Combine.

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{6 x^{2} \cdot 3}{5 \cdot 4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.8

Cancel the common factor of $6$ and $4$ .

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Step 3.8.1

Factor $2$ out of $6 x^{2} \cdot 3$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{2 (3 x^{2} \cdot 3)}{5 \cdot 4} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.8.2

Cancel the common factors.

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Step 3.8.2.1

Factor $2$ out of $5 \cdot 4$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{2 (3 x^{2} \cdot 3)}{2 (5 \cdot 2)} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.8.2.2

Cancel the common factor.

Step 3.8.2.3

Rewrite the expression.

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{3 x^{2} \cdot 3}{5 \cdot 2} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.9

Multiply $3$ by $3$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{5 \cdot 2} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.10

Multiply $5$ by $2$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - 2 x \frac{6 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.11

Multiply $- 2 x \frac{6 x^{2}}{5}$ .

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Step 3.11.1

Combine $- 2$ and $\frac{6 x^{2}}{5}$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} + x \frac{- 2 (6 x^{2})}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.11.2

Multiply $6$ by $- 2$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} + x \frac{- 12 x^{2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.11.3

Combine $x$ and $\frac{- 12 x^{2}}{5}$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} + \frac{x (- 12 x^{2})}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.11.4

Raise $x$ to the power of $1$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} + \frac{- 12 (x^{1} x^{2})}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.11.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} + \frac{- 12 x^{1 + 2}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.11.6

Add $1$ and $2$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} + \frac{- 12 x^{3}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.12

Move the negative in front of the fraction.

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} - 2 x (- \frac{2 x}{5}) - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.13

Multiply $- 2 x (- \frac{2 x}{5})$ .

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Step 3.13.1

Multiply $- 1$ by $- 2$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + 2 x \frac{2 x}{5} - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.13.2

Combine $2$ and $\frac{2 x}{5}$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + x \frac{2 (2 x)}{5} - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.13.3

Multiply $2$ by $2$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + x \frac{4 x}{5} - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.13.4

Combine $x$ and $\frac{4 x}{5}$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{x (4 x)}{5} - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.13.5

Raise $x$ to the power of $1$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 (x^{1} x)}{5} - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.13.6

Raise $x$ to the power of $1$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 (x^{1} x^{1})}{5} - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.13.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{1 + 1}}{5} - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.13.8

Add $1$ and $1$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - 2 x \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.14

Cancel the common factor of $2$ .

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Step 3.14.1

Factor $2$ out of $- 2 x$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} + 2 (- x) \frac{3}{4} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.14.2

Factor $2$ out of $4$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} + 2 (- x) \frac{3}{2 (2)} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.14.3

Cancel the common factor.

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} + 2 (- x) \frac{3}{2 \cdot 2} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.14.4

Rewrite the expression.

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - x \frac{3}{2} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.15

Combine $\frac{3}{2}$ and $x$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{3}{5} \cdot \frac{6 x^{2}}{5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.16

Multiply $- \frac{3}{5} \cdot \frac{6 x^{2}}{5}$ .

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Step 3.16.1

Multiply $\frac{6 x^{2}}{5}$ by $\frac{3}{5}$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{6 x^{2} \cdot 3}{5 \cdot 5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.16.2

Multiply $3$ by $6$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{5 \cdot 5} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.16.3

Multiply $5$ by $5$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} - \frac{3}{5} (- \frac{2 x}{5}) - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.17

Multiply $- \frac{3}{5} (- \frac{2 x}{5})$ .

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Step 3.17.1

Multiply $- 1$ by $- 1$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + 1 (\frac{3}{5}) \frac{2 x}{5} - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.17.2

Multiply $\frac{3}{5}$ by $1$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{3}{5} \cdot \frac{2 x}{5} - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.17.3

Multiply $\frac{3}{5}$ by $\frac{2 x}{5}$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{3 (2 x)}{5 \cdot 5} - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.17.4

Multiply $2$ by $3$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{6 x}{5 \cdot 5} - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.17.5

Multiply $5$ by $5$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{6 x}{25} - \frac{3}{5} \cdot \frac{3}{4}$

Step 3.18

Multiply $- \frac{3}{5} \cdot \frac{3}{4}$ .

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Step 3.18.1

Multiply $\frac{3}{4}$ by $\frac{3}{5}$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{6 x}{25} - \frac{3 \cdot 3}{4 \cdot 5}$

Step 3.18.2

Multiply $3$ by $3$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{6 x}{25} - \frac{9}{4 \cdot 5}$

Step 3.18.3

Multiply $4$ by $5$ .

$\frac{36 x^{4}}{25} - \frac{12 x^{3}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{6 x}{25} - \frac{9}{20}$

Step 4

To write $- \frac{12 x^{3}}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{36 x^{4}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{25} - \frac{12 x^{3}}{5} \cdot \frac{5}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{6 x}{25} - \frac{9}{20}$

Step 5

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{12 x^{3}}{5}$ by $\frac{5}{5}$ .

$\frac{36 x^{4}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{25} - \frac{12 x^{3} \cdot 5}{5 \cdot 5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{6 x}{25} - \frac{9}{20}$

Step 5.2

Multiply $5$ by $5$ .

$\frac{36 x^{4}}{25} + \frac{9 x^{2}}{10} - \frac{12 x^{3}}{25} - \frac{12 x^{3} \cdot 5}{25} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{6 x}{25} - \frac{9}{20}$

Step 6

Simplify terms.

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Step 6.1

Combine the numerators over the common denominator.

$\frac{36 x^{4}}{25} + \frac{9 x^{2}}{10} + \frac{- 12 x^{3} - 12 x^{3} \cdot 5}{25} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{18 x^{2}}{25} + \frac{6 x}{25} - \frac{9}{20}$

Step 6.2

Combine the numerators over the common denominator.

$\frac{36 x^{4} - 12 x^{3} - 12 x^{3} \cdot 5 - 18 x^{2} + 6 x}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 6.3

Multiply $5$ by $- 12$ .

$\frac{36 x^{4} - 12 x^{3} - 60 x^{3} - 18 x^{2} + 6 x}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 6.4

Subtract $60 x^{3}$ from $- 12 x^{3}$ .

$\frac{36 x^{4} - 72 x^{3} - 18 x^{2} + 6 x}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 7

Simplify each term.

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Step 7.1

Factor $6 x$ out of $36 x^{4} - 72 x^{3} - 18 x^{2} + 6 x$ .

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Step 7.1.1

Factor $6 x$ out of $36 x^{4}$ .

$\frac{6 x (6 x^{3}) - 72 x^{3} - 18 x^{2} + 6 x}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 7.1.2

Factor $6 x$ out of $- 72 x^{3}$ .

$\frac{6 x (6 x^{3}) + 6 x (- 12 x^{2}) - 18 x^{2} + 6 x}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 7.1.3

Factor $6 x$ out of $- 18 x^{2}$ .

$\frac{6 x (6 x^{3}) + 6 x (- 12 x^{2}) + 6 x (- 3 x) + 6 x}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 7.1.4

Factor $6 x$ out of $6 x$ .

$\frac{6 x (6 x^{3}) + 6 x (- 12 x^{2}) + 6 x (- 3 x) + 6 x (1)}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 7.1.5

Factor $6 x$ out of $6 x (6 x^{3}) + 6 x (- 12 x^{2})$ .

$\frac{6 x (6 x^{3} - 12 x^{2}) + 6 x (- 3 x) + 6 x (1)}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 7.1.6

Factor $6 x$ out of $6 x (6 x^{3} - 12 x^{2}) + 6 x (- 3 x)$ .

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x) + 6 x (1)}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 7.1.7

Factor $6 x$ out of $6 x (6 x^{3} - 12 x^{2} - 3 x) + 6 x (1)$ .

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1)}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} + \frac{- 3 x}{2} + \frac{- 9}{20}$

Step 7.2

Move the negative in front of the fraction.

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1)}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} - \frac{3 x}{2} + \frac{- 9}{20}$

Step 7.3

Move the negative in front of the fraction.

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1)}{25} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 8

To write $\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1)}{25}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1)}{25} \cdot \frac{2}{2} + \frac{9 x^{2}}{10} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 9

To write $\frac{9 x^{2}}{10}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1)}{25} \cdot \frac{2}{2} + \frac{9 x^{2}}{10} \cdot \frac{5}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 10

Write each expression with a common denominator of $50$ , by multiplying each by an appropriate factor of $1$ .

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Step 10.1

Multiply $\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1)}{25}$ by $\frac{2}{2}$ .

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1) \cdot 2}{25 \cdot 2} + \frac{9 x^{2}}{10} \cdot \frac{5}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 10.2

Multiply $25$ by $2$ .

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1) \cdot 2}{50} + \frac{9 x^{2}}{10} \cdot \frac{5}{5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 10.3

Multiply $\frac{9 x^{2}}{10}$ by $\frac{5}{5}$ .

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1) \cdot 2}{50} + \frac{9 x^{2} \cdot 5}{10 \cdot 5} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 10.4

Multiply $10$ by $5$ .

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1) \cdot 2}{50} + \frac{9 x^{2} \cdot 5}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 11

Combine the numerators over the common denominator.

$\frac{6 x (6 x^{3} - 12 x^{2} - 3 x + 1) \cdot 2 + 9 x^{2} \cdot 5}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12

Simplify the numerator.

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Step 12.1

Factor $3 x$ out of $6 x (6 x^{3} - 12 x^{2} - 3 x + 1) \cdot 2 + 9 x^{2} \cdot 5$ .

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Step 12.1.1

Factor $3 x$ out of $6 x (6 x^{3} - 12 x^{2} - 3 x + 1) \cdot 2$ .

$\frac{3 x ((2 (6 x^{3} - 12 x^{2} - 3 x + 1)) \cdot 2) + 9 x^{2} \cdot 5}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.1.2

Factor $3 x$ out of $9 x^{2} \cdot 5$ .

$\frac{3 x ((2 (6 x^{3} - 12 x^{2} - 3 x + 1)) \cdot 2) + 3 x (3 x \cdot 5)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.1.3

Factor $3 x$ out of $3 x ((2 (6 x^{3} - 12 x^{2} - 3 x + 1)) \cdot 2) + 3 x (3 x \cdot 5)$ .

$\frac{3 x ((2 (6 x^{3} - 12 x^{2} - 3 x + 1)) \cdot 2 + 3 x \cdot 5)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.2

Combine exponents.

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Step 12.2.1

Multiply $2$ by $2$ .

$\frac{3 x (4 (6 x^{3} - 12 x^{2} - 3 x + 1) + 3 x \cdot 5)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.2.2

Multiply $5$ by $3$ .

$\frac{3 x (4 (6 x^{3} - 12 x^{2} - 3 x + 1) + 15 x)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.3

Simplify each term.

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Step 12.3.1

Apply the distributive property.

$\frac{3 x (4 (6 x^{3}) + 4 (- 12 x^{2}) + 4 (- 3 x) + 4 \cdot 1 + 15 x)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.3.2

Simplify.

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Step 12.3.2.1

Multiply $6$ by $4$ .

$\frac{3 x (24 x^{3} + 4 (- 12 x^{2}) + 4 (- 3 x) + 4 \cdot 1 + 15 x)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.3.2.2

Multiply $- 12$ by $4$ .

$\frac{3 x (24 x^{3} - 48 x^{2} + 4 (- 3 x) + 4 \cdot 1 + 15 x)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.3.2.3

Multiply $- 3$ by $4$ .

$\frac{3 x (24 x^{3} - 48 x^{2} - 12 x + 4 \cdot 1 + 15 x)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.3.2.4

Multiply $4$ by $1$ .

$\frac{3 x (24 x^{3} - 48 x^{2} - 12 x + 4 + 15 x)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 12.4

Add $- 12 x$ and $15 x$ .

$\frac{3 x (24 x^{3} - 48 x^{2} + 3 x + 4)}{50} + \frac{4 x^{2}}{5} - \frac{3 x}{2} - \frac{9}{20}$

Step 13

To write $\frac{4 x^{2}}{5}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{3 x (24 x^{3} - 48 x^{2} + 3 x + 4)}{50} + \frac{4 x^{2}}{5} \cdot \frac{10}{10} - \frac{3 x}{2} - \frac{9}{20}$

Step 14

Write each expression with a common denominator of $50$ , by multiplying each by an appropriate factor of $1$ .

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Step 14.1

Multiply $\frac{4 x^{2}}{5}$ by $\frac{10}{10}$ .

$\frac{3 x (24 x^{3} - 48 x^{2} + 3 x + 4)}{50} + \frac{4 x^{2} \cdot 10}{5 \cdot 10} - \frac{3 x}{2} - \frac{9}{20}$

Step 14.2

Multiply $5$ by $10$ .

$\frac{3 x (24 x^{3} - 48 x^{2} + 3 x + 4)}{50} + \frac{4 x^{2} \cdot 10}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 15

Combine the numerators over the common denominator.

$\frac{3 x (24 x^{3} - 48 x^{2} + 3 x + 4) + 4 x^{2} \cdot 10}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16

Simplify the numerator.

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Step 16.1

Factor $x$ out of $3 x (24 x^{3} - 48 x^{2} + 3 x + 4) + 4 x^{2} \cdot 10$ .

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Step 16.1.1

Factor $x$ out of $3 x (24 x^{3} - 48 x^{2} + 3 x + 4)$ .

$\frac{x (3 (24 x^{3} - 48 x^{2} + 3 x + 4)) + 4 x^{2} \cdot 10}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16.1.2

Factor $x$ out of $4 x^{2} \cdot 10$ .

$\frac{x (3 (24 x^{3} - 48 x^{2} + 3 x + 4)) + x (4 x \cdot 10)}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16.1.3

Factor $x$ out of $x (3 (24 x^{3} - 48 x^{2} + 3 x + 4)) + x (4 x \cdot 10)$ .

$\frac{x (3 (24 x^{3} - 48 x^{2} + 3 x + 4) + 4 x \cdot 10)}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16.2

Apply the distributive property.

$\frac{x (3 (24 x^{3}) + 3 (- 48 x^{2}) + 3 (3 x) + 3 \cdot 4 + 4 x \cdot 10)}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16.3

Simplify.

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Step 16.3.1

Multiply $24$ by $3$ .

$\frac{x (72 x^{3} + 3 (- 48 x^{2}) + 3 (3 x) + 3 \cdot 4 + 4 x \cdot 10)}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16.3.2

Multiply $- 48$ by $3$ .

$\frac{x (72 x^{3} - 144 x^{2} + 3 (3 x) + 3 \cdot 4 + 4 x \cdot 10)}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16.3.3

Multiply $3$ by $3$ .

$\frac{x (72 x^{3} - 144 x^{2} + 9 x + 3 \cdot 4 + 4 x \cdot 10)}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16.3.4

Multiply $3$ by $4$ .

$\frac{x (72 x^{3} - 144 x^{2} + 9 x + 12 + 4 x \cdot 10)}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16.4

Multiply $10$ by $4$ .

$\frac{x (72 x^{3} - 144 x^{2} + 9 x + 12 + 40 x)}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 16.5

Add $9 x$ and $40 x$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x + 12)}{50} - \frac{3 x}{2} - \frac{9}{20}$

Step 17

To write $- \frac{3 x}{2}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x + 12)}{50} - \frac{3 x}{2} \cdot \frac{25}{25} - \frac{9}{20}$

Step 18

Write each expression with a common denominator of $50$ , by multiplying each by an appropriate factor of $1$ .

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Step 18.1

Multiply $\frac{3 x}{2}$ by $\frac{25}{25}$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x + 12)}{50} - \frac{3 x \cdot 25}{2 \cdot 25} - \frac{9}{20}$

Step 18.2

Multiply $2$ by $25$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x + 12)}{50} - \frac{3 x \cdot 25}{50} - \frac{9}{20}$

Step 19

Combine the numerators over the common denominator.

$\frac{x (72 x^{3} - 144 x^{2} + 49 x + 12) - 3 x \cdot 25}{50} - \frac{9}{20}$

Step 20

Simplify the numerator.

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Step 20.1

Factor $x$ out of $x (72 x^{3} - 144 x^{2} + 49 x + 12) - 3 x \cdot 25$ .

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Step 20.1.1

Factor $x$ out of $- 3 x \cdot 25$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x + 12) + x (- 3 \cdot 25)}{50} - \frac{9}{20}$

Step 20.1.2

Factor $x$ out of $x (72 x^{3} - 144 x^{2} + 49 x + 12) + x (- 3 \cdot 25)$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x + 12 - 3 \cdot 25)}{50} - \frac{9}{20}$

Step 20.2

Multiply $- 3$ by $25$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x + 12 - 75)}{50} - \frac{9}{20}$

Step 20.3

Subtract $75$ from $12$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63)}{50} - \frac{9}{20}$

Step 21

To write $\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63)}{50}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63)}{50} \cdot \frac{2}{2} - \frac{9}{20}$

Step 22

To write $- \frac{9}{20}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63)}{50} \cdot \frac{2}{2} - \frac{9}{20} \cdot \frac{5}{5}$

Step 23

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

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Step 23.1

Multiply $\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63)}{50}$ by $\frac{2}{2}$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63) \cdot 2}{50 \cdot 2} - \frac{9}{20} \cdot \frac{5}{5}$

Step 23.2

Multiply $50$ by $2$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63) \cdot 2}{100} - \frac{9}{20} \cdot \frac{5}{5}$

Step 23.3

Multiply $\frac{9}{20}$ by $\frac{5}{5}$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63) \cdot 2}{100} - \frac{9 \cdot 5}{20 \cdot 5}$

Step 23.4

Multiply $20$ by $5$ .

$\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63) \cdot 2}{100} - \frac{9 \cdot 5}{100}$

Step 24

Combine the numerators over the common denominator.

$\frac{x (72 x^{3} - 144 x^{2} + 49 x - 63) \cdot 2 - 9 \cdot 5}{100}$

Step 25

Simplify the numerator.

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Step 25.1

Apply the distributive property.

$\frac{(x (72 x^{3}) + x (- 144 x^{2}) + x (49 x) + x \cdot - 63) \cdot 2 - 9 \cdot 5}{100}$

Step 25.2

Simplify.

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Step 25.2.1

Rewrite using the commutative property of multiplication.

$\frac{(72 x \cdot x^{3} + x (- 144 x^{2}) + x (49 x) + x \cdot - 63) \cdot 2 - 9 \cdot 5}{100}$

Step 25.2.2

Rewrite using the commutative property of multiplication.

$\frac{(72 x \cdot x^{3} - 144 x \cdot x^{2} + x (49 x) + x \cdot - 63) \cdot 2 - 9 \cdot 5}{100}$

Step 25.2.3

Rewrite using the commutative property of multiplication.

$\frac{(72 x \cdot x^{3} - 144 x \cdot x^{2} + 49 x \cdot x + x \cdot - 63) \cdot 2 - 9 \cdot 5}{100}$

Step 25.2.4

Move $- 63$ to the left of $x$ .

$\frac{(72 x \cdot x^{3} - 144 x \cdot x^{2} + 49 x \cdot x - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3

Simplify each term.

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Step 25.3.1

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 25.3.1.1

Move $x^{3}$ .

$\frac{(72 (x^{3} x) - 144 x \cdot x^{2} + 49 x \cdot x - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3.1.2

Multiply $x^{3}$ by $x$ .

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Step 25.3.1.2.1

Raise $x$ to the power of $1$ .

$\frac{(72 (x^{3} x^{1}) - 144 x \cdot x^{2} + 49 x \cdot x - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(72 x^{3 + 1} - 144 x \cdot x^{2} + 49 x \cdot x - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3.1.3

Add $3$ and $1$ .

$\frac{(72 x^{4} - 144 x \cdot x^{2} + 49 x \cdot x - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3.2

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 25.3.2.1

Move $x^{2}$ .

$\frac{(72 x^{4} - 144 (x^{2} x) + 49 x \cdot x - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3.2.2

Multiply $x^{2}$ by $x$ .

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Step 25.3.2.2.1

Raise $x$ to the power of $1$ .

$\frac{(72 x^{4} - 144 (x^{2} x^{1}) + 49 x \cdot x - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(72 x^{4} - 144 x^{2 + 1} + 49 x \cdot x - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3.2.3

Add $2$ and $1$ .

$\frac{(72 x^{4} - 144 x^{3} + 49 x \cdot x - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3.3

Multiply $x$ by $x$ by adding the exponents.

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Step 25.3.3.1

Move $x$ .

$\frac{(72 x^{4} - 144 x^{3} + 49 (x \cdot x) - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.3.3.2

Multiply $x$ by $x$ .

$\frac{(72 x^{4} - 144 x^{3} + 49 x^{2} - 63 \cdot x) \cdot 2 - 9 \cdot 5}{100}$

$\frac{(72 x^{4} - 144 x^{3} + 49 x^{2} - 63 x) \cdot 2 - 9 \cdot 5}{100}$

Step 25.4

Apply the distributive property.

$\frac{72 x^{4} \cdot 2 - 144 x^{3} \cdot 2 + 49 x^{2} \cdot 2 - 63 x \cdot 2 - 9 \cdot 5}{100}$

Step 25.5

Simplify.

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Step 25.5.1

Multiply $2$ by $72$ .

$\frac{144 x^{4} - 144 x^{3} \cdot 2 + 49 x^{2} \cdot 2 - 63 x \cdot 2 - 9 \cdot 5}{100}$

Step 25.5.2

Multiply $2$ by $- 144$ .

$\frac{144 x^{4} - 288 x^{3} + 49 x^{2} \cdot 2 - 63 x \cdot 2 - 9 \cdot 5}{100}$

Step 25.5.3

Multiply $2$ by $49$ .

$\frac{144 x^{4} - 288 x^{3} + 98 x^{2} - 63 x \cdot 2 - 9 \cdot 5}{100}$

Step 25.5.4

Multiply $2$ by $- 63$ .

$\frac{144 x^{4} - 288 x^{3} + 98 x^{2} - 126 x - 9 \cdot 5}{100}$

Step 25.6

Multiply $- 9$ by $5$ .

$\frac{144 x^{4} - 288 x^{3} + 98 x^{2} - 126 x - 45}{100}$