Solve left(x^2+2xright)^2-2left(x^2+2xright)

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply -2 by x^{2}+2x.

$$x^{4}+4x^{3}+4x^{2}-2x^{2}-4x$$

Combine 4x^{2} and -2x^{2} to get 2x^{2}.

$$x^{4}+4x^{3}+2x^{2}-4x$$

Expand

$$x^{4}+4x^{3}+2x^{2}-4x$$

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply -2 by x^{2}+2x.

$$x^{4}+4x^{3}+4x^{2}-2x^{2}-4x$$

Combine 4x^{2} and -2x^{2} to get 2x^{2}.

$$x^{4}+4x^{3}+2x^{2}-4x$$