Algebra Examples

$3 x (x^{2} - 4) (5 - 3 x)$

Step 1

Apply the distributive property.

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

Step 2

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

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

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

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Step 2.2.1

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

$(3 (x^{2} x^{1}) + 3 x \cdot - 4) (5 - 3 x)$

Step 2.2.2

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

$(3 x^{2 + 1} + 3 x \cdot - 4) (5 - 3 x)$

Step 2.3

Add $2$ and $1$ .

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

Step 3

Multiply $- 4$ by $3$ .

$(3 x^{3} - 12 x) (5 - 3 x)$

Step 4

Expand $(3 x^{3} - 12 x) (5 - 3 x)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$3 x^{3} (5 - 3 x) - 12 x (5 - 3 x)$

Step 4.2

Apply the distributive property.

$3 x^{3} \cdot 5 + 3 x^{3} (- 3 x) - 12 x (5 - 3 x)$

Step 4.3

Apply the distributive property.

$3 x^{3} \cdot 5 + 3 x^{3} (- 3 x) - 12 x \cdot 5 - 12 x (- 3 x)$

Step 5

Simplify terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $5$ by $3$ .

$15 x^{3} + 3 x^{3} (- 3 x) - 12 x \cdot 5 - 12 x (- 3 x)$

Step 5.1.2

Rewrite using the commutative property of multiplication.

$15 x^{3} + 3 \cdot - 3 x^{3} x - 12 x \cdot 5 - 12 x (- 3 x)$

Step 5.1.3

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

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Step 5.1.3.1

Move $x$ .

$15 x^{3} + 3 \cdot - 3 (x \cdot x^{3}) - 12 x \cdot 5 - 12 x (- 3 x)$

Step 5.1.3.2

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

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Step 5.1.3.2.1

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

$15 x^{3} + 3 \cdot - 3 (x^{1} x^{3}) - 12 x \cdot 5 - 12 x (- 3 x)$

Step 5.1.3.2.2

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

$15 x^{3} + 3 \cdot - 3 x^{1 + 3} - 12 x \cdot 5 - 12 x (- 3 x)$

Step 5.1.3.3

Add $1$ and $3$ .

$15 x^{3} + 3 \cdot - 3 x^{4} - 12 x \cdot 5 - 12 x (- 3 x)$

Step 5.1.4

Multiply $3$ by $- 3$ .

$15 x^{3} - 9 x^{4} - 12 x \cdot 5 - 12 x (- 3 x)$

Step 5.1.5

Multiply $5$ by $- 12$ .

$15 x^{3} - 9 x^{4} - 60 x - 12 x (- 3 x)$

Step 5.1.6

Rewrite using the commutative property of multiplication.

$15 x^{3} - 9 x^{4} - 60 x - 12 \cdot - 3 x \cdot x$

Step 5.1.7

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

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Step 5.1.7.1

Move $x$ .

$15 x^{3} - 9 x^{4} - 60 x - 12 \cdot - 3 (x \cdot x)$

Step 5.1.7.2

Multiply $x$ by $x$ .

$15 x^{3} - 9 x^{4} - 60 x - 12 \cdot - 3 x^{2}$

Step 5.1.8

Multiply $- 12$ by $- 3$ .

$15 x^{3} - 9 x^{4} - 60 x + 36 x^{2}$

Step 5.2

Simplify the expression.

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Step 5.2.1

Move $- 60 x$ .

$15 x^{3} - 9 x^{4} + 36 x^{2} - 60 x$

Step 5.2.2

Reorder $15 x^{3}$ and $- 9 x^{4}$ .

$- 9 x^{4} + 15 x^{3} + 36 x^{2} - 60 x$