Solve -5x^2-20v^2+20xv

$$- 5 x ^ { 2 } - 20 v ^ { 2 } + 20 x v$$

Factor

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

Solution Steps

Factor out 5.

$$5\left(-x^{2}-4v^{2}+4xv\right)$$

Consider -x^{2}-4v^{2}+4xv. Consider -x^{2}-4v^{2}+4xv as a polynomial over variable x.

$$-x^{2}+4vx-4v^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -x^{2} and n divides the constant factor -4v^{2}. One such factor is x-2v. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression.

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

Evaluate

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