Solve left(4x^2-5right)^2

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

Expand

$$16x^{4}-40x^{2}+25$$

Solution Steps

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

$$16\left(x^{2}\right)^{2}-40x^{2}+25$$

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

$$16x^{4}-40x^{2}+25$$

Evaluate

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

Solution Steps

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

$$16\left(x^{2}\right)^{2}-40x^{2}+25$$

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

$$16x^{4}-40x^{2}+25$$