Basic Math Examples

$\frac{m^{2} + 16 m + 64}{m + 9} \cdot \frac{m - 4}{4 - m}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $64$ as $8^{2}$ .

$\frac{m^{2} + 16 m + 8^{2}}{m + 9} \cdot \frac{m - 4}{4 - m}$

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$16 m = 2 \cdot m \cdot 8$

Step 1.3

Rewrite the polynomial.

$\frac{m^{2} + 2 \cdot m \cdot 8 + 8^{2}}{m + 9} \cdot \frac{m - 4}{4 - m}$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = m$ and $b = 8$ .

$\frac{{(m + 8)}^{2}}{m + 9} \cdot \frac{m - 4}{4 - m}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $m - 4$ and $4 - m$ .

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Step 2.1.1

Factor $- 1$ out of $m$ .

$\frac{{(m + 8)}^{2}}{m + 9} \cdot \frac{- 1 (- m) - 4}{4 - m}$

Step 2.1.2

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{{(m + 8)}^{2}}{m + 9} \cdot \frac{- 1 (- m) - 1 (4)}{4 - m}$

Step 2.1.3

Factor $- 1$ out of $- 1 (- m) - 1 (4)$ .

$\frac{{(m + 8)}^{2}}{m + 9} \cdot \frac{- 1 (- m + 4)}{4 - m}$

Step 2.1.4

Reorder terms.

$\frac{{(m + 8)}^{2}}{m + 9} \cdot \frac{- 1 (- m + 4)}{- m + 4}$

Step 2.1.5

Cancel the common factor.

$\frac{{(m + 8)}^{2}}{m + 9} \cdot \frac{- 1 (- m + 4)}{- m + 4}$

Step 2.1.6

Divide $- 1$ by $1$ .

$\frac{{(m + 8)}^{2}}{m + 9} \cdot - 1$

Step 2.2

Combine $\frac{{(m + 8)}^{2}}{m + 9}$ and $- 1$ .

$\frac{{(m + 8)}^{2} \cdot - 1}{m + 9}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Move $- 1$ to the left of ${(m + 8)}^{2}$ .

$\frac{- 1 \cdot {(m + 8)}^{2}}{m + 9}$

Step 2.3.2

Move the negative in front of the fraction.

$- \frac{{(m + 8)}^{2}}{m + 9}$