Solve left(16x^2-9right)^2

$${ \left(16 { x }^{ 2 } -9 \right) }^{ 2 }$$

Expand

$$256x^{4}-288x^{2}+81$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(16x^{2}-9\right)^{2}.

$$256\left(x^{2}\right)^{2}-288x^{2}+81$$

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

$$256x^{4}-288x^{2}+81$$

Evaluate

$$\left(16x^{2}-9\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(16x^{2}-9\right)^{2}.

$$256\left(x^{2}\right)^{2}-288x^{2}+81$$

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

$$256x^{4}-288x^{2}+81$$