Solve (x^6+2x^5)^(2)

$$( x ^ { 6 } + 2 x ^ { 5 } ) ^ { ( 2 ) }$$

Evaluate

$$\left(x+2\right)^{2}x^{10}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{6}+2x^{5}\right)^{2}.

$$\left(x^{6}\right)^{2}+4x^{6}x^{5}+4\left(x^{5}\right)^{2}$$

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

$$x^{12}+4x^{6}x^{5}+4\left(x^{5}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$x^{12}+4x^{11}+4\left(x^{5}\right)^{2}$$

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

$$x^{12}+4x^{11}+4x^{10}$$

Expand

$$x^{12}+4x^{11}+4x^{10}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{6}+2x^{5}\right)^{2}.

$$\left(x^{6}\right)^{2}+4x^{6}x^{5}+4\left(x^{5}\right)^{2}$$

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

$$x^{12}+4x^{6}x^{5}+4\left(x^{5}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$x^{12}+4x^{11}+4\left(x^{5}\right)^{2}$$

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

$$x^{12}+4x^{11}+4x^{10}$$