Solve (5x^2+8)^2

$$( 5 x ^ { 2 } + 8 ) ^ { 2 }$$

Expand

$$25x^{4}+80x^{2}+64$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x^{2}+8\right)^{2}.

$$25\left(x^{2}\right)^{2}+80x^{2}+64$$

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

$$25x^{4}+80x^{2}+64$$

Evaluate

$$\left(5x^{2}+8\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x^{2}+8\right)^{2}.

$$25\left(x^{2}\right)^{2}+80x^{2}+64$$

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

$$25x^{4}+80x^{2}+64$$