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

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

Evaluate

$$\left(x-y\right)\left(5x-4y\right)$$

Solution Steps

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

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

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

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

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

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

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

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

Combine -8xy and -xy to get -9xy.

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

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$5x^{2}-9xy+4y^{2}$$

Expand

$$5x^{2}-9xy+4y^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

Combine -8xy and -xy to get -9xy.

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

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$5x^{2}-9xy+4y^{2}$$