Solve (9-2x^5)^2

$$( 9 - 2 x ^ { 5 } ) ^ { 2 }$$

Expand

$$4x^{10}-36x^{5}+81$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(9-2x^{5}\right)^{2}.

$$81-36x^{5}+4\left(x^{5}\right)^{2}$$

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

$$81-36x^{5}+4x^{10}$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(9-2x^{5}\right)^{2}.

$$81-36x^{5}+4\left(x^{5}\right)^{2}$$

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

$$81-36x^{5}+4x^{10}$$