Finite Math Examples

$\frac{a d - b d}{a^{2} + 2 a b + b^{2}}$

Step 1

Factor $d$ out of $a d - b d$ .

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Step 1.1

Factor $d$ out of $a d$ .

$\frac{d a - b d}{a^{2} + 2 a b + b^{2}}$

Step 1.2

Factor $d$ out of $- b d$ .

$\frac{d a + d (- b)}{a^{2} + 2 a b + b^{2}}$

Step 1.3

Factor $d$ out of $d a + d (- b)$ .

$\frac{d (a - b)}{a^{2} + 2 a b + b^{2}}$

Step 2

Factor using the perfect square rule.

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Step 2.1

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

$2 a b = 2 \cdot a \cdot b$

Step 2.2

Rewrite the polynomial.

$\frac{d (a - b)}{a^{2} + 2 \cdot a \cdot b + b^{2}}$

Step 2.3

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

$\frac{d (a - b)}{{(a + b)}^{2}}$