Solve 2x^2-4xy+2xy-4y^2

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

Factor

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

Solution Steps

Factor out 2.

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

Consider x^{2}-2xy+xy-2y^{2}. Multiply and combine like terms.

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

Consider x^{2}-xy-2y^{2}. Consider x^{2}-xy-2y^{2} as a polynomial over variable x.

$$x^{2}-yx-2y^{2}$$

Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{2} and m divides the constant factor -2y^{2}. One such factor is x-2y. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression.

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

Evaluate

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

Solution Steps

Combine -4xy and 2xy to get -2xy.

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