Basic Math Examples

$\frac{3}{4} \cdot (a^{2} (\frac{9}{2} a - a) (\frac{2}{3} a - \frac{1}{6} a))$

Step 1

Combine $\frac{9}{2}$ and $a$ .

$\frac{3}{4} \cdot (a^{2} (\frac{9 a}{2} - a) (\frac{2}{3} a - \frac{1}{6} a))$

Step 2

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

$\frac{3}{4} \cdot (a^{2} (\frac{9 a}{2} - a \cdot \frac{2}{2}) (\frac{2}{3} a - \frac{1}{6} a))$

Step 3

Simplify terms.

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Step 3.1

Combine $- a$ and $\frac{2}{2}$ .

$\frac{3}{4} \cdot (a^{2} (\frac{9 a}{2} + \frac{- a \cdot 2}{2}) (\frac{2}{3} a - \frac{1}{6} a))$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3}{4} \cdot (a^{2} \frac{9 a - a \cdot 2}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 4

Simplify the numerator.

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Step 4.1

Factor $a$ out of $9 a - a \cdot 2$ .

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Step 4.1.1

Factor $a$ out of $9 a$ .

$\frac{3}{4} \cdot (a^{2} \frac{a \cdot 9 - a \cdot 2}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 4.1.2

Factor $a$ out of $- a \cdot 2$ .

$\frac{3}{4} \cdot (a^{2} \frac{a \cdot 9 + a (- 1 \cdot 2)}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 4.1.3

Factor $a$ out of $a \cdot 9 + a (- 1 \cdot 2)$ .

$\frac{3}{4} \cdot (a^{2} \frac{a (9 - 1 \cdot 2)}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 4.2

Multiply $- 1$ by $2$ .

$\frac{3}{4} \cdot (a^{2} \frac{a (9 - 2)}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 4.3

Subtract $2$ from $9$ .

$\frac{3}{4} \cdot (a^{2} \frac{a \cdot 7}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 5

Move $7$ to the left of $a$ .

$\frac{3}{4} \cdot (a^{2} \frac{7 \cdot a}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 6

Multiply $a^{2} \frac{7 a}{2}$ .

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Step 6.1

Combine $a^{2}$ and $\frac{7 a}{2}$ .

$\frac{3}{4} \cdot (\frac{a^{2} (7 a)}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 6.2

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

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Step 6.2.1

Move $a$ .

$\frac{3}{4} \cdot (\frac{a \cdot a^{2} \cdot 7}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 6.2.2

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

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Step 6.2.2.1

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

$\frac{3}{4} \cdot (\frac{a^{1} a^{2} \cdot 7}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 6.2.2.2

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

$\frac{3}{4} \cdot (\frac{a^{1 + 2} \cdot 7}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 6.2.3

Add $1$ and $2$ .

$\frac{3}{4} \cdot (\frac{a^{3} \cdot 7}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 7

Move $7$ to the left of $a^{3}$ .

$\frac{3}{4} \cdot (\frac{7 \cdot a^{3}}{2} (\frac{2}{3} a - \frac{1}{6} a))$

Step 8

Simplify each term.

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Step 8.1

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

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} (\frac{2 a}{3} - \frac{1}{6} a))$

Step 8.2

Combine $a$ and $\frac{1}{6}$ .

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} (\frac{2 a}{3} - \frac{a}{6}))$

Step 9

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

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} (\frac{2 a}{3} \cdot \frac{2}{2} - \frac{a}{6}))$

Step 10

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 10.1

Multiply $\frac{2 a}{3}$ by $\frac{2}{2}$ .

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} (\frac{2 a \cdot 2}{3 \cdot 2} - \frac{a}{6}))$

Step 10.2

Multiply $3$ by $2$ .

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} (\frac{2 a \cdot 2}{6} - \frac{a}{6}))$

Step 11

Combine the numerators over the common denominator.

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} \cdot \frac{2 a \cdot 2 - a}{6})$

Step 12

Simplify the numerator.

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Step 12.1

Factor $a$ out of $2 a \cdot 2 - a$ .

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Step 12.1.1

Factor $a$ out of $2 a \cdot 2$ .

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} \cdot \frac{a (2 \cdot 2) - a}{6})$

Step 12.1.2

Factor $a$ out of $- a$ .

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} \cdot \frac{a (2 \cdot 2) + a \cdot - 1}{6})$

Step 12.1.3

Factor $a$ out of $a (2 \cdot 2) + a \cdot - 1$ .

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} \cdot \frac{a (2 \cdot 2 - 1)}{6})$

Step 12.2

Multiply $2$ by $2$ .

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} \cdot \frac{a (4 - 1)}{6})$

Step 12.3

Subtract $1$ from $4$ .

$\frac{3}{4} \cdot (\frac{7 a^{3}}{2} \cdot \frac{a \cdot 3}{6})$

Step 13

Combine fractions.

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Step 13.1

Combine.

$\frac{3}{4} \cdot \frac{7 a^{3} (a \cdot 3)}{2 \cdot 6}$

Step 13.2

Combine.

$\frac{3 (7 a^{3} (a \cdot 3))}{4 (2 \cdot 6)}$

Step 14

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

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Step 14.1

Move $a$ .

$\frac{3 (7 (a \cdot a^{3}) \cdot 3)}{4 (2 \cdot 6)}$

Step 14.2

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

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Step 14.2.1

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

$\frac{3 (7 (a^{1} a^{3}) \cdot 3)}{4 (2 \cdot 6)}$

Step 14.2.2

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

$\frac{3 (7 a^{1 + 3} \cdot 3)}{4 (2 \cdot 6)}$

Step 14.3

Add $1$ and $3$ .

$\frac{3 (7 a^{4} \cdot 3)}{4 (2 \cdot 6)}$

Step 15

Cancel the common factors.

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Step 15.1

Factor $3$ out of $4 (2 \cdot 6)$ .

$\frac{3 (7 a^{4} \cdot 3)}{3 (4 (2 \cdot 2))}$

Step 15.2

Cancel the common factor.

$\frac{3 (7 a^{4} \cdot 3)}{3 (4 (2 \cdot 2))}$

Step 15.3

Rewrite the expression.

$\frac{7 a^{4} \cdot 3}{4 (2 \cdot 2)}$

Step 16

Multiply $3$ by $7$ .

$\frac{21 a^{4}}{4 \cdot 2 \cdot 2}$

Step 17

Simplify the denominator.

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Step 17.1

Multiply $4$ by $2$ .

$\frac{21 a^{4}}{8 \cdot 2}$

Step 17.2

Multiply $8$ by $2$ .

$\frac{21 a^{4}}{16}$