Precalculus Examples

$4 {(x + h)}^{2} + 3 (x + h) + 2$

Step 1

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

$4 ((x + h) (x + h)) + 3 (x + h) + 2$

Step 2

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

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Step 2.1

Apply the distributive property.

$4 (x (x + h) + h (x + h)) + 3 (x + h) + 2$

Step 2.2

Apply the distributive property.

$4 (x \cdot x + x h + h (x + h)) + 3 (x + h) + 2$

Step 2.3

Apply the distributive property.

$4 (x \cdot x + x h + h x + h \cdot h) + 3 (x + h) + 2$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

$4 (x^{2} + x h + h x + h \cdot h) + 3 (x + h) + 2$

Step 3.1.2

Multiply $h$ by $h$ .

$4 (x^{2} + x h + h x + h^{2}) + 3 (x + h) + 2$

Step 3.2

Add $x h$ and $h x$ .

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Step 3.2.1

Reorder $x$ and $h$ .

$4 (x^{2} + h x + h x + h^{2}) + 3 (x + h) + 2$

Step 3.2.2

Add $h x$ and $h x$ .

$4 (x^{2} + 2 h x + h^{2}) + 3 (x + h) + 2$

Step 4

Apply the distributive property.

$4 x^{2} + 4 (2 h x) + 4 h^{2} + 3 (x + h) + 2$

Step 5

Multiply $2$ by $4$ .

$4 x^{2} + 8 (h x) + 4 h^{2} + 3 (x + h) + 2$

Step 6

Remove parentheses.

$4 x^{2} + 8 h x + 4 h^{2} + 3 (x + h) + 2$

Step 7

Apply the distributive property.

$4 x^{2} + 8 h x + 4 h^{2} + 3 x + 3 h + 2$