Precalculus Examples

$4 x^{2} - 64 x + 256$

Step 1

Factor $4$ out of $4 x^{2} - 64 x + 256$ .

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Step 1.1

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

$4 (x^{2}) - 64 x + 256$

Step 1.2

Factor $4$ out of $- 64 x$ .

$4 (x^{2}) + 4 (- 16 x) + 256$

Step 1.3

Factor $4$ out of $256$ .

$4 x^{2} + 4 (- 16 x) + 4 \cdot 64$

Step 1.4

Factor $4$ out of $4 x^{2} + 4 (- 16 x)$ .

$4 (x^{2} - 16 x) + 4 \cdot 64$

Step 1.5

Factor $4$ out of $4 (x^{2} - 16 x) + 4 \cdot 64$ .

$4 (x^{2} - 16 x + 64)$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $64$ as $8^{2}$ .

$4 (x^{2} - 16 x + 8^{2})$

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.

$16 x = 2 \cdot x \cdot 8$

Step 2.3

Rewrite the polynomial.

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

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 8$ .

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