Solve (5d^4+8)^2

$$( 5 d ^ { 4 } + 8 ) ^ { 2 }$$

Expand

$$25d^{8}+80d^{4}+64$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5d^{4}+8\right)^{2}.

$$25\left(d^{4}\right)^{2}+80d^{4}+64$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$25d^{8}+80d^{4}+64$$

Evaluate

$$\left(5d^{4}+8\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5d^{4}+8\right)^{2}.

$$25\left(d^{4}\right)^{2}+80d^{4}+64$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$25d^{8}+80d^{4}+64$$