Solve (8x^4+1)^2=

$$( 8 x ^ { 4 } + 1 ) ^ { 2 } =$$

Evaluate

$$\left(8x^{4}+1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8x^{4}+1\right)^{2}.

$$64\left(x^{4}\right)^{2}+16x^{4}+1$$

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

$$64x^{8}+16x^{4}+1$$

Expand

$$64x^{8}+16x^{4}+1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8x^{4}+1\right)^{2}.

$$64\left(x^{4}\right)^{2}+16x^{4}+1$$

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

$$64x^{8}+16x^{4}+1$$