Solve (2-4x^2)^2

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

Evaluate

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

Solution Steps

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

$$4-16x^{2}+16\left(x^{2}\right)^{2}$$

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

$$4-16x^{2}+16x^{4}$$

Expand

$$16x^{4}-16x^{2}+4$$

Solution Steps

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

$$4-16x^{2}+16\left(x^{2}\right)^{2}$$

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

$$4-16x^{2}+16x^{4}$$