Solve (1+6y^3)^2

$$( 1 + 6 y ^ { 3 } ) ^ { 2 }$$

Evaluate

$$\left(6y^{3}+1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+6y^{3}\right)^{2}.

$$1+12y^{3}+36\left(y^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$1+12y^{3}+36y^{6}$$

Expand

$$36y^{6}+12y^{3}+1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+6y^{3}\right)^{2}.

$$1+12y^{3}+36\left(y^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$1+12y^{3}+36y^{6}$$