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

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

Evaluate

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

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}.

$$\left(x^{3}+12x^{2}+48x+64\right)\left(x^{2}+4\right)$$

Use the distributive property to multiply x^{3}+12x^{2}+48x+64 by x^{2}+4 and combine like terms.

$$x^{5}+52x^{3}+12x^{4}+112x^{2}+192x+256$$

Expand

$$x^{5}+12x^{4}+52x^{3}+112x^{2}+192x+256$$

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}.

$$\left(x^{3}+12x^{2}+48x+64\right)\left(x^{2}+4\right)$$

Use the distributive property to multiply x^{3}+12x^{2}+48x+64 by x^{2}+4 and combine like terms.

$$x^{5}+52x^{3}+12x^{4}+112x^{2}+192x+256$$