Solve E=(z+z)^2(z+1)(z+3)-5z(z+4)-27

$$E = ( z + z ) ^ { 2 } ( z + 1 ) ( z + 3 ) - 5 z ( z + 4 ) - 27$$

Solve for E

$$E=4z^{4}+16z^{3}+7z^{2}-20z-27$$

Solution Steps

Combine z and z to get 2z.

$$E=\left(2z\right)^{2}\left(z+1\right)\left(z+3\right)-5z\left(z+4\right)-27$$

Expand \left(2z\right)^{2}.

$$E=2^{2}z^{2}\left(z+1\right)\left(z+3\right)-5z\left(z+4\right)-27$$

Calculate 2 to the power of 2 and get 4.

$$E=4z^{2}\left(z+1\right)\left(z+3\right)-5z\left(z+4\right)-27$$

Use the distributive property to multiply 4z^{2} by z+1.

$$E=\left(4z^{3}+4z^{2}\right)\left(z+3\right)-5z\left(z+4\right)-27$$

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

$$E=4z^{4}+16z^{3}+12z^{2}-5z\left(z+4\right)-27$$

Use the distributive property to multiply -5z by z+4.

$$E=4z^{4}+16z^{3}+12z^{2}-5z^{2}-20z-27$$

Combine 12z^{2} and -5z^{2} to get 7z^{2}.

$$E=4z^{4}+16z^{3}+7z^{2}-20z-27$$