Solve 5x(x-y)-2(y-x)^2=

$$5 x ( x - y ) - 2 ( y - x ) ^ { 2 } =$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 5x by x-y.

$$5x^{2}-5xy-2\left(y-x\right)^{2}$$

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

$$5x^{2}-5xy-2\left(y^{2}-2yx+x^{2}\right)$$

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

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

Combine -5xy and 4yx to get -xy.

$$5x^{2}-xy-2y^{2}-2x^{2}$$

Combine 5x^{2} and -2x^{2} to get 3x^{2}.

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

Expand

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

Solution Steps

Use the distributive property to multiply 5x by x-y.

$$5x^{2}-5xy-2\left(y-x\right)^{2}$$

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

$$5x^{2}-5xy-2\left(y^{2}-2yx+x^{2}\right)$$

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

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

Combine -5xy and 4yx to get -xy.

$$5x^{2}-xy-2y^{2}-2x^{2}$$

Combine 5x^{2} and -2x^{2} to get 3x^{2}.

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