Algebra Examples

$4 x^{2} - 8 x + 4$

Step 1

Factor $4$ out of $4 x^{2} - 8 x + 4$ .

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Step 1.1

Factor $4$ out of $4 x^{2}$ .

$4 (x^{2}) - 8 x + 4$

Step 1.2

Factor $4$ out of $- 8 x$ .

$4 (x^{2}) + 4 (- 2 x) + 4$

Step 1.3

Factor $4$ out of $4$ .

$4 (x^{2}) + 4 (- 2 x) + 4 (1)$

Step 1.4

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

$4 (x^{2} - 2 x) + 4 (1)$

Step 1.5

Factor $4$ out of $4 (x^{2} - 2 x) + 4 (1)$ .

$4 (x^{2} - 2 x + 1)$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$4 (x^{2} - 2 x + 1^{2})$

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.

$2 x = 2 \cdot x \cdot 1$

Step 2.3

Rewrite the polynomial.

$4 (x^{2} - 2 \cdot x \cdot 1 + 1^{2})$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 1$ .

$4 {(x - 1)}^{2}$