Precalculus Examples

$2 x^{2} - 4 x$

Step 1

Factor out the $2$

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

Step 2

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $x$ by $2$ and square the result.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Cancel the common factor.

${(- \frac{2}{2})}^{2}$

Step 2.1.2

Rewrite the expression.

${(- 1 \cdot 1)}^{2}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Multiply $- 1$ by $1$ .

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

Step 2.2.2

Raise $- 1$ to the power of $2$ .

$1$

Step 3

Add $1$ to get the perfect square trinomial.

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

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

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

Step 4.2

Simplify.

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Step 4.2.1

Multiply $- 2$ by $2$ .

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

Step 4.2.2

Multiply $2$ by $1$ .

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