Solve left(x^2-25right)^2

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

Expand

$$x^{4}-50x^{2}+625$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-25\right)^{2}.

$$\left(x^{2}\right)^{2}-50x^{2}+625$$

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

$$x^{4}-50x^{2}+625$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-25\right)^{2}.

$$\left(x^{2}\right)^{2}-50x^{2}+625$$

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

$$x^{4}-50x^{2}+625$$