Solve 8y^2(1-y^2)^2

$$8 y ^ { 2 } ( 1 - y ^ { 2 } ) ^ { 2 }$$

Evaluate

$$8\left(y-y^{3}\right)^{2}$$

Solution Steps

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

$$8y^{2}\left(1-2y^{2}+\left(y^{2}\right)^{2}\right)$$

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

$$8y^{2}\left(1-2y^{2}+y^{4}\right)$$

Use the distributive property to multiply 8y^{2} by 1-2y^{2}+y^{4}.

$$8y^{2}-16y^{4}+8y^{6}$$

Expand

$$8y^{6}-16y^{4}+8y^{2}$$

Solution Steps

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

$$8y^{2}\left(1-2y^{2}+\left(y^{2}\right)^{2}\right)$$

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

$$8y^{2}\left(1-2y^{2}+y^{4}\right)$$

Use the distributive property to multiply 8y^{2} by 1-2y^{2}+y^{4}.

$$8y^{2}-16y^{4}+8y^{6}$$