Pre-Algebra Examples

$8 x^{2} + 16 x y + 8 y^{2}$

Step 1

Factor $8$ out of $8 x^{2} + 16 x y + 8 y^{2}$ .

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Step 1.1

Factor $8$ out of $8 x^{2}$ .

$8 (x^{2}) + 16 x y + 8 y^{2}$

Step 1.2

Factor $8$ out of $16 x y$ .

$8 (x^{2}) + 8 (2 x y) + 8 y^{2}$

Step 1.3

Factor $8$ out of $8 y^{2}$ .

$8 (x^{2}) + 8 (2 x y) + 8 (y^{2})$

Step 1.4

Factor $8$ out of $8 (x^{2}) + 8 (2 x y)$ .

$8 (x^{2} + 2 x y) + 8 (y^{2})$

Step 1.5

Factor $8$ out of $8 (x^{2} + 2 x y) + 8 (y^{2})$ .

$8 (x^{2} + 2 x y + y^{2})$

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.

$2 x y = 2 \cdot x \cdot y$

Step 2.2

Rewrite the polynomial.

$8 (x^{2} + 2 \cdot x \cdot y + y^{2})$

Step 2.3

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

$8 {(x + y)}^{2}$