Solve (-x^5+4x)^2

$$( - x ^ { 5 } + 4 x ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-x^{5}+4x\right)^{2}.

$$\left(-x^{5}\right)^{2}+8\left(-x^{5}\right)x+16x^{2}$$

Calculate -x^{5} to the power of 2 and get \left(x^{5}\right)^{2}.

$$\left(x^{5}\right)^{2}+8\left(-x^{5}\right)x+16x^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$x^{10}+8\left(-x^{5}\right)x+16x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$x^{10}+8\left(-1\right)x^{6}+16x^{2}$$

Multiply 8 and -1 to get -8.

$$x^{10}-8x^{6}+16x^{2}$$

Expand

$$x^{10}-8x^{6}+16x^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-x^{5}+4x\right)^{2}.

$$\left(-x^{5}\right)^{2}+8\left(-x^{5}\right)x+16x^{2}$$

Calculate -x^{5} to the power of 2 and get \left(x^{5}\right)^{2}.

$$\left(x^{5}\right)^{2}+8\left(-x^{5}\right)x+16x^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$x^{10}+8\left(-x^{5}\right)x+16x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$x^{10}+8\left(-1\right)x^{6}+16x^{2}$$

Multiply 8 and -1 to get -8.

$$x^{10}-8x^{6}+16x^{2}$$