Solve (x^2+4x)^2-(x^2+4x)-20

$$( x ^ { 2 } + 4 x ) ^ { 2 } - ( x ^ { 2 } + 4 x ) - 20$$

Evaluate

$$\left(x-1\right)\left(x+5\right)\left(x+2\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+4x\right)^{2}.

$$\left(x^{2}\right)^{2}+8x^{2}x+16x^{2}-\left(x^{2}+4x\right)-20$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}+8x^{2}x+16x^{2}-\left(x^{2}+4x\right)-20$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}+8x^{3}+16x^{2}-\left(x^{2}+4x\right)-20$$

To find the opposite of x^{2}+4x, find the opposite of each term.

$$x^{4}+8x^{3}+16x^{2}-x^{2}-4x-20$$

Combine 16x^{2} and -x^{2} to get 15x^{2}.

$$x^{4}+8x^{3}+15x^{2}-4x-20$$

Expand

$$x^{4}+8x^{3}+15x^{2}-4x-20$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+4x\right)^{2}.

$$\left(x^{2}\right)^{2}+8x^{2}x+16x^{2}-\left(x^{2}+4x\right)-20$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}+8x^{2}x+16x^{2}-\left(x^{2}+4x\right)-20$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}+8x^{3}+16x^{2}-\left(x^{2}+4x\right)-20$$

To find the opposite of x^{2}+4x, find the opposite of each term.

$$x^{4}+8x^{3}+16x^{2}-x^{2}-4x-20$$

Combine 16x^{2} and -x^{2} to get 15x^{2}.

$$x^{4}+8x^{3}+15x^{2}-4x-20$$