Solve 9y^2-left(2x-yright)^2

$$9 { y }^{ 2 } - { \left(2x-y \right) }^{ 2 }$$

Evaluate

$$4\left(2y-x\right)\left(x+y\right)$$

Solution Steps

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

$$9y^{2}-\left(4x^{2}-4xy+y^{2}\right)$$

To find the opposite of 4x^{2}-4xy+y^{2}, find the opposite of each term.

$$9y^{2}-4x^{2}+4xy-y^{2}$$

Combine 9y^{2} and -y^{2} to get 8y^{2}.

$$8y^{2}-4x^{2}+4xy$$

Expand

$$8y^{2}+4xy-4x^{2}$$

Solution Steps

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

$$9y^{2}-\left(4x^{2}-4xy+y^{2}\right)$$

To find the opposite of 4x^{2}-4xy+y^{2}, find the opposite of each term.

$$9y^{2}-4x^{2}+4xy-y^{2}$$

Combine 9y^{2} and -y^{2} to get 8y^{2}.

$$8y^{2}-4x^{2}+4xy$$