Solve (-x^3+x)^2

$$( - x ^ { 3 } + x ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-x^{3}+x\right)^{2}.

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

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{6}+2\left(-x^{3}\right)x+x^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{6}+2\left(-1\right)x^{4}+x^{2}$$

Multiply 2 and -1 to get -2.

$$x^{6}-2x^{4}+x^{2}$$

Expand

$$x^{6}-2x^{4}+x^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-x^{3}+x\right)^{2}.

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

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{6}+2\left(-x^{3}\right)x+x^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{6}+2\left(-1\right)x^{4}+x^{2}$$

Multiply 2 and -1 to get -2.

$$x^{6}-2x^{4}+x^{2}$$