Basic Math Examples

$(y + 4) \div \frac{y^{2} + 8 y + 16}{a b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(y + 4) \frac{a b}{y^{2} + 8 y + 16}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$(y + 4) \frac{a b}{y^{2} + 8 y + 4^{2}}$

Step 2.2

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

$8 y = 2 \cdot y \cdot 4$

Step 2.3

Rewrite the polynomial.

$(y + 4) \frac{a b}{y^{2} + 2 \cdot y \cdot 4 + 4^{2}}$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = 4$ .

$(y + 4) \frac{a b}{{(y + 4)}^{2}}$

Step 3

Cancel the common factor of $y + 4$ .

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Step 3.1

Factor $y + 4$ out of ${(y + 4)}^{2}$ .

$(y + 4) \frac{a b}{(y + 4) (y + 4)}$

Step 3.2

Cancel the common factor.

$(y + 4) \frac{a b}{(y + 4) (y + 4)}$

Step 3.3

Rewrite the expression.

$\frac{a b}{y + 4}$