Solve (8x^6+8)^2

$$( 8 x ^ { 6 } + 8 ) ^ { 2 }$$

Evaluate

$$64\left(x^{6}+1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8x^{6}+8\right)^{2}.

$$64\left(x^{6}\right)^{2}+128x^{6}+64$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$64x^{12}+128x^{6}+64$$

Expand

$$64x^{12}+128x^{6}+64$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8x^{6}+8\right)^{2}.

$$64\left(x^{6}\right)^{2}+128x^{6}+64$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$64x^{12}+128x^{6}+64$$