Algebra Examples

$- \frac{35 a x^{2}}{12 b^{2}} \cdot \frac{8 a b}{21 x y}$

Step 1

Cancel the common factor of $7 x$ .

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Step 1.1

Move the leading negative in $- \frac{35 a x^{2}}{12 b^{2}}$ into the numerator.

$\frac{- 35 a x^{2}}{12 b^{2}} \cdot \frac{8 a b}{21 x y}$

Step 1.2

Factor $7 x$ out of $- 35 a x^{2}$ .

$\frac{7 x (- 5 a x)}{12 b^{2}} \cdot \frac{8 a b}{21 x y}$

Step 1.3

Factor $7 x$ out of $21 x y$ .

$\frac{7 x (- 5 a x)}{12 b^{2}} \cdot \frac{8 a b}{7 x (3 y)}$

Step 1.4

Cancel the common factor.

$\frac{7 x (- 5 a x)}{12 b^{2}} \cdot \frac{8 a b}{7 x (3 y)}$

Step 1.5

Rewrite the expression.

$\frac{- 5 a x}{12 b^{2}} \cdot \frac{8 a b}{3 y}$

Step 2

Cancel the common factor of $4 b$ .

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Step 2.1

Factor $4 b$ out of $12 b^{2}$ .

$\frac{- 5 a x}{4 b (3 b)} \cdot \frac{8 a b}{3 y}$

Step 2.2

Factor $4 b$ out of $8 a b$ .

$\frac{- 5 a x}{4 b (3 b)} \cdot \frac{4 b (2 a)}{3 y}$

Step 2.3

Cancel the common factor.

$\frac{- 5 a x}{4 b (3 b)} \cdot \frac{4 b (2 a)}{3 y}$

Step 2.4

Rewrite the expression.

$\frac{- 5 a x}{3 b} \cdot \frac{2 a}{3 y}$

Step 3

Multiply $\frac{- 5 a x}{3 b}$ by $\frac{2 a}{3 y}$ .

$\frac{- 5 a x (2 a)}{3 b (3 y)}$

Step 4

Multiply $2$ by $- 5$ .

$\frac{- 10 a x a}{3 b (3 y)}$

Step 5

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

$\frac{- 10 (a^{1} a) x}{3 b (3 y)}$

Step 6

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

$\frac{- 10 (a^{1} a^{1}) x}{3 b (3 y)}$

Step 7

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

$\frac{- 10 a^{1 + 1} x}{3 b (3 y)}$

Step 8

Add $1$ and $1$ .

$\frac{- 10 a^{2} x}{3 b (3 y)}$

Step 9

Multiply $3$ by $3$ .

$\frac{- 10 a^{2} x}{9 b y}$

Step 10

Move the negative in front of the fraction.

$- \frac{10 a^{2} x}{9 b y}$