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

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

Evaluate

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

Solution Steps

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

$$x^{3}\left(x^{3}+6x^{2}+12x+8\right)$$

Use the distributive property to multiply x^{3} by x^{3}+6x^{2}+12x+8.

$$x^{6}+6x^{5}+12x^{4}+8x^{3}$$

Expand

$$x^{6}+6x^{5}+12x^{4}+8x^{3}$$

Solution Steps

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

$$x^{3}\left(x^{3}+6x^{2}+12x+8\right)$$

Use the distributive property to multiply x^{3} by x^{3}+6x^{2}+12x+8.

$$x^{6}+6x^{5}+12x^{4}+8x^{3}$$