Solve 10x^2-5xy-5y^2

$$10 x ^ { 2 } - 5 x y - 5 y ^ { 2 }$$

Factor

$$5\left(x-y\right)\left(2x+y\right)$$

Solution Steps

Factor out 5.

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

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

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

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

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

Rewrite the complete factored expression.

$$5\left(2x+y\right)\left(x-y\right)$$

Evaluate

$$5\left(x-y\right)\left(2x+y\right)$$