Solve z^3(z+2)^2-4z^3+2

$$z ^ { 3 } ( z + 2 ) ^ { 2 } - 4 z ^ { 3 } + 2$$

Evaluate

$$z^{5}+4z^{4}+2$$

Solution Steps

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

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

Use the distributive property to multiply z^{3} by z^{2}+4z+4.

$$z^{5}+4z^{4}+4z^{3}-4z^{3}+2$$

Combine 4z^{3} and -4z^{3} to get 0.

$$z^{5}+4z^{4}+2$$

Expand

$$z^{5}+4z^{4}+2$$

Solution Steps

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

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

Use the distributive property to multiply z^{3} by z^{2}+4z+4.

$$z^{5}+4z^{4}+4z^{3}-4z^{3}+2$$

Combine 4z^{3} and -4z^{3} to get 0.

$$z^{5}+4z^{4}+2$$