Solve (x^2+2x)^2-18(x^2+2x)+45

$$( x ^ { 2 } + 2 x ) ^ { 2 } - 18 ( x ^ { 2 } + 2 x ) + 45$$

Evaluate

$$\left(x-1\right)\left(x+5\right)\left(x^{2}-9\right)$$

Solution Steps

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

$$\left(x^{2}\right)^{2}+4x^{2}x+4x^{2}-18\left(x^{2}+2x\right)+45$$

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

$$x^{4}+4x^{2}x+4x^{2}-18\left(x^{2}+2x\right)+45$$

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

$$x^{4}+4x^{3}+4x^{2}-18\left(x^{2}+2x\right)+45$$

Use the distributive property to multiply -18 by x^{2}+2x.

$$x^{4}+4x^{3}+4x^{2}-18x^{2}-36x+45$$

Combine 4x^{2} and -18x^{2} to get -14x^{2}.

$$x^{4}+4x^{3}-14x^{2}-36x+45$$

Expand

$$x^{4}+4x^{3}-14x^{2}-36x+45$$

Solution Steps

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

$$\left(x^{2}\right)^{2}+4x^{2}x+4x^{2}-18\left(x^{2}+2x\right)+45$$

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

$$x^{4}+4x^{2}x+4x^{2}-18\left(x^{2}+2x\right)+45$$

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

$$x^{4}+4x^{3}+4x^{2}-18\left(x^{2}+2x\right)+45$$

Use the distributive property to multiply -18 by x^{2}+2x.

$$x^{4}+4x^{3}+4x^{2}-18x^{2}-36x+45$$

Combine 4x^{2} and -18x^{2} to get -14x^{2}.

$$x^{4}+4x^{3}-14x^{2}-36x+45$$