Find P(s(x)) P(x)=3x^2+1 and s(a)=4a+4

$P (x) = 3 x^{2} + 1$ and $s (a) = 4 a + 4$

Step 1

Set up the composite result function.

$P (s (a))$

Step 2

Evaluate $P (4 a + 4)$ by substituting in the value of $s$ into $P$ .

$P (4 a + 4) = 3 {(4 a + 4)}^{2} + 1$

Step 3

Simplify each term.

Rewrite ${(4 a + 4)}^{2}$ as $(4 a + 4) (4 a + 4)$ .

$P (4 a + 4) = 3 ((4 a + 4) (4 a + 4)) + 1$

Expand $(4 a + 4) (4 a + 4)$ using the FOIL Method.

Apply the distributive property.

$P (4 a + 4) = 3 (4 a (4 a + 4) + 4 (4 a + 4)) + 1$

Apply the distributive property.

$P (4 a + 4) = 3 (4 a (4 a) + 4 a \cdot 4 + 4 (4 a + 4)) + 1$

Apply the distributive property.

$P (4 a + 4) = 3 (4 a (4 a) + 4 a \cdot 4 + 4 (4 a) + 4 \cdot 4) + 1$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$P (4 a + 4) = 3 (4 \cdot (4 a \cdot a) + 4 a \cdot 4 + 4 (4 a) + 4 \cdot 4) + 1$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$P (4 a + 4) = 3 (4 \cdot (4 (a \cdot a)) + 4 a \cdot 4 + 4 (4 a) + 4 \cdot 4) + 1$

Multiply $a$ by $a$ .

$P (4 a + 4) = 3 (4 \cdot (4 a^{2}) + 4 a \cdot 4 + 4 (4 a) + 4 \cdot 4) + 1$

Multiply $4$ by $4$ .

$P (4 a + 4) = 3 (16 a^{2} + 4 a \cdot 4 + 4 (4 a) + 4 \cdot 4) + 1$

Multiply $4$ by $4$ .

$P (4 a + 4) = 3 (16 a^{2} + 16 a + 4 (4 a) + 4 \cdot 4) + 1$

Multiply $4$ by $4$ .

$P (4 a + 4) = 3 (16 a^{2} + 16 a + 16 a + 4 \cdot 4) + 1$

Multiply $4$ by $4$ .

$P (4 a + 4) = 3 (16 a^{2} + 16 a + 16 a + 16) + 1$

Add $16 a$ and $16 a$ .

$P (4 a + 4) = 3 (16 a^{2} + 32 a + 16) + 1$

Apply the distributive property.

$P (4 a + 4) = 3 (16 a^{2}) + 3 (32 a) + 3 \cdot 16 + 1$

Simplify.

Multiply $16$ by $3$ .

$P (4 a + 4) = 48 a^{2} + 3 (32 a) + 3 \cdot 16 + 1$

Multiply $32$ by $3$ .

$P (4 a + 4) = 48 a^{2} + 96 a + 3 \cdot 16 + 1$

Multiply $3$ by $16$ .

$P (4 a + 4) = 48 a^{2} + 96 a + 48 + 1$

Step 4

Add $48$ and $1$ .

$P (4 a + 4) = 48 a^{2} + 96 a + 49$

Find P(s(x)) P(x)=3x^2+1 and s(a)=4a+4

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