Solve f(x)=(x^5+x)^2

$$f ( x ) = ( x ^ { 5 } + x ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$x^{10}+2x^{5}x+x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$x^{10}+2x^{6}+x^{2}$$

Expand

$$x^{10}+2x^{6}+x^{2}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$x^{10}+2x^{5}x+x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$x^{10}+2x^{6}+x^{2}$$