Solve (5y^2+y)^2

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

Evaluate

$$\left(y\left(5y+1\right)\right)^{2}$$

Solution Steps

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

$$25\left(y^{2}\right)^{2}+10y^{2}y+y^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$25y^{4}+10y^{2}y+y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$25y^{4}+10y^{3}+y^{2}$$

Expand

$$25y^{4}+10y^{3}+y^{2}$$

Solution Steps

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

$$25\left(y^{2}\right)^{2}+10y^{2}y+y^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$25y^{4}+10y^{2}y+y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$25y^{4}+10y^{3}+y^{2}$$