Solve p(x)=2(x+4)^3+3

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

Evaluate

$$2\left(x+4\right)^{3}+3$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+4\right)^{3}.

$$2\left(x^{3}+12x^{2}+48x+64\right)+3$$

Use the distributive property to multiply 2 by x^{3}+12x^{2}+48x+64.

$$2x^{3}+24x^{2}+96x+128+3$$

Add 128 and 3 to get 131.

$$2x^{3}+24x^{2}+96x+131$$

Expand

$$2x^{3}+24x^{2}+96x+131$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+4\right)^{3}.

$$2\left(x^{3}+12x^{2}+48x+64\right)+3$$

Use the distributive property to multiply 2 by x^{3}+12x^{2}+48x+64.

$$2x^{3}+24x^{2}+96x+128+3$$

Add 128 and 3 to get 131.

$$2x^{3}+24x^{2}+96x+131$$