Solve 4x^2-(x-2y)^2

$$4 x ^ { 2 } - ( x - 2 y ) ^ { 2 }$$

Evaluate

$$\left(3x-2y\right)\left(x+2y\right)$$

Solution Steps

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

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

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

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

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}+4xy-4y^{2}$$

Expand

$$3x^{2}+4xy-4y^{2}$$

Solution Steps

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

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

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

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

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}+4xy-4y^{2}$$