Solve (-x^2-x)^2

$$( - x ^ { 2 } - x ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

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

Multiply -2 and -1 to get 2.

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

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

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

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

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

Expand

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

Solution Steps

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

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

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

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

Multiply -2 and -1 to get 2.

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

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

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

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

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