Solve 5(5x^2-1)^2

$$5 ( 5 x ^ { 2 } - 1 ) ^ { 2 }$$

Expand

$$125x^{4}-50x^{2}+5$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5x^{2}-1\right)^{2}.

$$5\left(25\left(x^{2}\right)^{2}-10x^{2}+1\right)$$

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

$$5\left(25x^{4}-10x^{2}+1\right)$$

Use the distributive property to multiply 5 by 25x^{4}-10x^{2}+1.

$$125x^{4}-50x^{2}+5$$

Evaluate

$$5\left(5x^{2}-1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5x^{2}-1\right)^{2}.

$$5\left(25\left(x^{2}\right)^{2}-10x^{2}+1\right)$$

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

$$5\left(25x^{4}-10x^{2}+1\right)$$

Use the distributive property to multiply 5 by 25x^{4}-10x^{2}+1.

$$125x^{4}-50x^{2}+5$$