Algebra Examples

$2 x^{2} - 40 x + 200$

Step 1

Factor $2$ out of $2 x^{2} - 40 x + 200$ .

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Step 1.1

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

$2 (x^{2}) - 40 x + 200$

Step 1.2

Factor $2$ out of $- 40 x$ .

$2 (x^{2}) + 2 (- 20 x) + 200$

Step 1.3

Factor $2$ out of $200$ .

$2 x^{2} + 2 (- 20 x) + 2 \cdot 100$

Step 1.4

Factor $2$ out of $2 x^{2} + 2 (- 20 x)$ .

$2 (x^{2} - 20 x) + 2 \cdot 100$

Step 1.5

Factor $2$ out of $2 (x^{2} - 20 x) + 2 \cdot 100$ .

$2 (x^{2} - 20 x + 100)$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $100$ as $10^{2}$ .

$2 (x^{2} - 20 x + 10^{2})$

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.

$20 x = 2 \cdot x \cdot 10$

Step 2.3

Rewrite the polynomial.

$2 (x^{2} - 2 \cdot x \cdot 10 + 10^{2})$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 10$ .

$2 {(x - 10)}^{2}$