Basic Math Examples

$\frac{a^{2} + 2 a b + b^{2}}{3 a + 3 b}$

Step 1

Factor using the perfect square rule.

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Step 1.1

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 1.2

Rewrite the polynomial.

$\frac{a^{2} + 2 \cdot a \cdot b + b^{2}}{3 a + 3 b}$

Step 1.3

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

$\frac{{(a + b)}^{2}}{3 a + 3 b}$

Step 2

Simplify terms.

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Step 2.1

Factor $3$ out of $3 a + 3 b$ .

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Step 2.1.1

Factor $3$ out of $3 a$ .

$\frac{{(a + b)}^{2}}{3 (a) + 3 b}$

Step 2.1.2

Factor $3$ out of $3 b$ .

$\frac{{(a + b)}^{2}}{3 (a) + 3 (b)}$

Step 2.1.3

Factor $3$ out of $3 (a) + 3 (b)$ .

$\frac{{(a + b)}^{2}}{3 (a + b)}$

Step 2.2

Cancel the common factor of ${(a + b)}^{2}$ and $a + b$ .

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Step 2.2.1

Factor $a + b$ out of ${(a + b)}^{2}$ .

$\frac{(a + b) (a + b)}{3 (a + b)}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $a + b$ out of $3 (a + b)$ .

$\frac{(a + b) (a + b)}{(a + b) \cdot 3}$

Step 2.2.2.2

Cancel the common factor.

$\frac{(a + b) (a + b)}{(a + b) \cdot 3}$

Step 2.2.2.3

Rewrite the expression.

$\frac{a + b}{3}$