Precalculus Examples

$2 {(x + h)}^{2} - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(x + h)}^{2}$ as $(x + h) (x + h)$ .

$2 ((x + h) (x + h)) - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.2

Expand $(x + h) (x + h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 (x (x + h) + h (x + h)) - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.2.2

Apply the distributive property.

$2 (x \cdot x + x h + h (x + h)) - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.2.3

Apply the distributive property.

$2 (x \cdot x + x h + h x + h \cdot h) - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$2 (x^{2} + x h + h x + h \cdot h) - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.3.1.2

Multiply $h$ by $h$ .

$2 (x^{2} + x h + h x + h^{2}) - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.3.2

Add $x h$ and $h x$ .

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Step 1.3.2.1

Reorder $x$ and $h$ .

$2 (x^{2} + h x + h x + h^{2}) - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.3.2.2

Add $h x$ and $h x$ .

$2 (x^{2} + 2 h x + h^{2}) - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.4

Apply the distributive property.

$2 x^{2} + 2 (2 h x) + 2 h^{2} - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.5

Multiply $2$ by $2$ .

$2 x^{2} + 4 (h x) + 2 h^{2} - 6 (x + h) - (2 x^{2} - 6 x)$

Step 1.6

Apply the distributive property.

$2 x^{2} + 4 h x + 2 h^{2} - 6 x - 6 h - (2 x^{2} - 6 x)$

Step 1.7

Apply the distributive property.

$2 x^{2} + 4 h x + 2 h^{2} - 6 x - 6 h - (2 x^{2}) - (- 6 x)$

Step 1.8

Multiply $2$ by $- 1$ .

$2 x^{2} + 4 h x + 2 h^{2} - 6 x - 6 h - 2 x^{2} - (- 6 x)$

Step 1.9

Multiply $- 6$ by $- 1$ .

$2 x^{2} + 4 h x + 2 h^{2} - 6 x - 6 h - 2 x^{2} + 6 x$

Step 2

Combine the opposite terms in $2 x^{2} + 4 h x + 2 h^{2} - 6 x - 6 h - 2 x^{2} + 6 x$ .

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Step 2.1

Subtract $2 x^{2}$ from $2 x^{2}$ .

$4 h x + 2 h^{2} - 6 x - 6 h + 0 + 6 x$

Step 2.2

Add $4 h x + 2 h^{2} - 6 x - 6 h$ and $0$ .

$4 h x + 2 h^{2} - 6 x - 6 h + 6 x$

Step 2.3

Add $- 6 x$ and $6 x$ .

$4 h x + 2 h^{2} - 6 h + 0$

Step 2.4

Add $4 h x + 2 h^{2} - 6 h$ and $0$ .

$4 h x + 2 h^{2} - 6 h$