Find P(d(x)) P(x)=x^3-8 d(x)=x+2

$P (x) = x^{3} - 8$ $d (x) = x + 2$

Set up the composite result function.

$P (d (x))$

Evaluate $P (x + 2)$ by substituting in the value of $d$ into $P$ .

$P (x + 2) = {(x + 2)}^{3} - 8$

Simplify each term.

Use the Binomial Theorem.

$P (x + 2) = x^{3} + 3 x^{2} \cdot 2 + 3 x \cdot 2^{2} + 2^{3} - 8$

Simplify each term.

Multiply $2$ by $3$ .

$P (x + 2) = x^{3} + 6 x^{2} + 3 x \cdot 2^{2} + 2^{3} - 8$

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

$P (x + 2) = x^{3} + 6 x^{2} + 3 x \cdot 4 + 2^{3} - 8$

Multiply $4$ by $3$ .

$P (x + 2) = x^{3} + 6 x^{2} + 12 x + 2^{3} - 8$

Raise $2$ to the power of $3$ .

$P (x + 2) = x^{3} + 6 x^{2} + 12 x + 8 - 8$

Combine the opposite terms in $x^{3} + 6 x^{2} + 12 x + 8 - 8$ .

Subtract $8$ from $8$ .

$P (x + 2) = x^{3} + 6 x^{2} + 12 x + 0$

Add $x^{3} + 6 x^{2} + 12 x$ and $0$ .

$P (x + 2) = x^{3} + 6 x^{2} + 12 x$