Solve -8xy^2-40xyz-50xz^2=

$$- 8 x y ^ { 2 } - 40 x y z - 50 x z ^ { 2 } =$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(-4xy^{2}-20xyz-25xz^{2}\right)$$

Consider -4xy^{2}-20xyz-25xz^{2}. Factor out x.

$$x\left(-4y^{2}-20yz-25z^{2}\right)$$

Consider -4y^{2}-20yz-25z^{2}. Consider -4y^{2}-20yz-25z^{2} as a polynomial over variable y.

$$-4y^{2}-20zy-25z^{2}$$

Find one factor of the form ky^{m}+n, where ky^{m} divides the monomial with the highest power -4y^{2} and n divides the constant factor -25z^{2}. One such factor is 2y+5z. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression.

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

Evaluate

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