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

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

Evaluate

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

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}.

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

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

$$x^{4}+14x^{3}+72x^{2}+160x+128$$

Expand

$$x^{4}+14x^{3}+72x^{2}+160x+128$$

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}.

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

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

$$x^{4}+14x^{3}+72x^{2}+160x+128$$