Solve (5+9y^8)^2

$$( 5 + 9 y ^ { 8 } ) ^ { 2 }$$

Evaluate

$$\left(9y^{8}+5\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5+9y^{8}\right)^{2}.

$$25+90y^{8}+81\left(y^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$25+90y^{8}+81y^{16}$$

Expand

$$81y^{16}+90y^{8}+25$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5+9y^{8}\right)^{2}.

$$25+90y^{8}+81\left(y^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$25+90y^{8}+81y^{16}$$