Precalculus Examples

$w (x) = 4 x^{2} - 5 x + 4$ , $w (3 + x)$

Step 1

Replace the variable $x$ with $3 + x$ in the expression.

$w (3 + x) = 4 {(3 + x)}^{2} - 5 (3 + x) + 4$

Step 2

Simplify $4 {(3 + x)}^{2} - 5 (3 + x) + 4$ .

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Step 2.1

Remove parentheses.

$4 {(3 + x)}^{2} - 5 (3 + x) + 4$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite ${(3 + x)}^{2}$ as $(3 + x) (3 + x)$ .

$4 ((3 + x) (3 + x)) - 5 (3 + x) + 4$

Step 2.2.2

Expand $(3 + x) (3 + x)$ using the FOIL Method.

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Step 2.2.2.1

Apply the distributive property.

$4 (3 (3 + x) + x (3 + x)) - 5 (3 + x) + 4$

Step 2.2.2.2

Apply the distributive property.

$4 (3 \cdot 3 + 3 x + x (3 + x)) - 5 (3 + x) + 4$

Step 2.2.2.3

Apply the distributive property.

$4 (3 \cdot 3 + 3 x + x \cdot 3 + x \cdot x) - 5 (3 + x) + 4$

Step 2.2.3

Simplify and combine like terms.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Multiply $3$ by $3$ .

$4 (9 + 3 x + x \cdot 3 + x \cdot x) - 5 (3 + x) + 4$

Step 2.2.3.1.2

Move $3$ to the left of $x$ .

$4 (9 + 3 x + 3 \cdot x + x \cdot x) - 5 (3 + x) + 4$

Step 2.2.3.1.3

Multiply $x$ by $x$ .

$4 (9 + 3 x + 3 x + x^{2}) - 5 (3 + x) + 4$

Step 2.2.3.2

Add $3 x$ and $3 x$ .

$4 (9 + 6 x + x^{2}) - 5 (3 + x) + 4$

Step 2.2.4

Apply the distributive property.

$4 \cdot 9 + 4 (6 x) + 4 x^{2} - 5 (3 + x) + 4$

Step 2.2.5

Simplify.

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Step 2.2.5.1

Multiply $4$ by $9$ .

$36 + 4 (6 x) + 4 x^{2} - 5 (3 + x) + 4$

Step 2.2.5.2

Multiply $6$ by $4$ .

$36 + 24 x + 4 x^{2} - 5 (3 + x) + 4$

Step 2.2.6

Apply the distributive property.

$36 + 24 x + 4 x^{2} - 5 \cdot 3 - 5 x + 4$

Step 2.2.7

Multiply $- 5$ by $3$ .

$36 + 24 x + 4 x^{2} - 15 - 5 x + 4$

Step 2.3

Simplify by adding terms.

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Step 2.3.1

Subtract $15$ from $36$ .

$24 x + 4 x^{2} + 21 - 5 x + 4$

Step 2.3.2

Subtract $5 x$ from $24 x$ .

$19 x + 4 x^{2} + 21 + 4$

Step 2.3.3

Simplify the expression.

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Step 2.3.3.1

Add $21$ and $4$ .

$19 x + 4 x^{2} + 25$

Step 2.3.3.2

Reorder $19 x$ and $4 x^{2}$ .

$4 x^{2} + 19 x + 25$