Solve (5A^2-1)^2

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

Expand

$$25A^{4}-10A^{2}+1$$

Solution Steps

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

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

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

$$25A^{4}-10A^{2}+1$$

Evaluate

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

Solution Steps

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

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

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

$$25A^{4}-10A^{2}+1$$