Solve (6x^2-x^4)^2

$$( 6 x ^ { 2 } - x ^ { 4 } ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x^{2}-x^{4}\right)^{2}.

$$36\left(x^{2}\right)^{2}-12x^{2}x^{4}+\left(x^{4}\right)^{2}$$

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

$$36x^{4}-12x^{2}x^{4}+\left(x^{4}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$36x^{4}-12x^{6}+\left(x^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$36x^{4}-12x^{6}+x^{8}$$

Expand

$$x^{8}-12x^{6}+36x^{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x^{2}-x^{4}\right)^{2}.

$$36\left(x^{2}\right)^{2}-12x^{2}x^{4}+\left(x^{4}\right)^{2}$$

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

$$36x^{4}-12x^{2}x^{4}+\left(x^{4}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$36x^{4}-12x^{6}+\left(x^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$36x^{4}-12x^{6}+x^{8}$$