Solve y=(x^6+x)^2

$$y = ( x ^ { 6 } + x ) ^ { 2 }$$

Solve for y

$$y=\left(x^{6}+x\right)^{2}$$

Solution Steps

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

$$y=\left(x^{6}\right)^{2}+2x^{6}x+x^{2}$$

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

$$y=x^{12}+2x^{6}x+x^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$y=x^{12}+2x^{7}+x^{2}$$