Precalculus Examples

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

Step 1

Set up the composite result function.

$p (D (x))$

Step 2

Evaluate $p (x + 3)$ by substituting in the value of $D$ into $p$ .

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

Step 3

Simplify each term.

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

Apply the distributive property.

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

Step 3.2.2

Apply the distributive property.

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

Step 3.2.3

Apply the distributive property.

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

Step 3.3

Simplify and combine like terms.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply $x$ by $x$ .

$p (x + 3) = 3 (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3) + 5 (x + 3) - 4$

Step 3.3.1.2

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

$p (x + 3) = 3 (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3) + 5 (x + 3) - 4$

Step 3.3.1.3

Multiply $3$ by $3$ .

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

Step 3.3.2

Add $3 x$ and $3 x$ .

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

Step 3.4

Apply the distributive property.

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

Step 3.5

Simplify.

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Step 3.5.1

Multiply $6$ by $3$ .

$p (x + 3) = 3 x^{2} + 18 x + 3 \cdot 9 + 5 (x + 3) - 4$

Step 3.5.2

Multiply $3$ by $9$ .

$p (x + 3) = 3 x^{2} + 18 x + 27 + 5 (x + 3) - 4$

Step 3.6

Apply the distributive property.

$p (x + 3) = 3 x^{2} + 18 x + 27 + 5 x + 5 \cdot 3 - 4$

Step 3.7

Multiply $5$ by $3$ .

$p (x + 3) = 3 x^{2} + 18 x + 27 + 5 x + 15 - 4$

Step 4

Simplify by adding terms.

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Step 4.1

Add $18 x$ and $5 x$ .

$p (x + 3) = 3 x^{2} + 23 x + 27 + 15 - 4$

Step 4.2

Simplify by adding and subtracting.

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Step 4.2.1

Add $27$ and $15$ .

$p (x + 3) = 3 x^{2} + 23 x + 42 - 4$

Step 4.2.2

Subtract $4$ from $42$ .

$p (x + 3) = 3 x^{2} + 23 x + 38$