Solve 4left(x-yright)left(x+yright)-3left(x-yright)^2

$$4 \left( x-y \right) \left( x+y \right) -3 { \left(x-y \right) }^{ 2 }$$

Evaluate

$$\left(x-y\right)\left(x+7y\right)$$

Solution Steps

Use the distributive property to multiply 4 by x-y.

$$\left(4x-4y\right)\left(x+y\right)-3\left(x-y\right)^{2}$$

Use the distributive property to multiply 4x-4y by x+y and combine like terms.

$$4x^{2}-4y^{2}-3\left(x-y\right)^{2}$$

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

$$4x^{2}-4y^{2}-3\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply -3 by x^{2}-2xy+y^{2}.

$$4x^{2}-4y^{2}-3x^{2}+6xy-3y^{2}$$

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

$$x^{2}-4y^{2}+6xy-3y^{2}$$

Combine -4y^{2} and -3y^{2} to get -7y^{2}.

$$x^{2}-7y^{2}+6xy$$

Expand

$$x^{2}+6xy-7y^{2}$$

Solution Steps

Use the distributive property to multiply 4 by x-y.

$$\left(4x-4y\right)\left(x+y\right)-3\left(x-y\right)^{2}$$

Use the distributive property to multiply 4x-4y by x+y and combine like terms.

$$4x^{2}-4y^{2}-3\left(x-y\right)^{2}$$

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

$$4x^{2}-4y^{2}-3\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply -3 by x^{2}-2xy+y^{2}.

$$4x^{2}-4y^{2}-3x^{2}+6xy-3y^{2}$$

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

$$x^{2}-4y^{2}+6xy-3y^{2}$$

Combine -4y^{2} and -3y^{2} to get -7y^{2}.

$$x^{2}-7y^{2}+6xy$$