Solve -5b^2-40bc-80c^2

$$- 5 b ^ { 2 } - 40 b c - 80 c ^ { 2 }$$

Factor

$$-5\left(b+4c\right)^{2}$$

Solution Steps

Factor out 5.

$$5\left(-b^{2}-8bc-16c^{2}\right)$$

Consider -b^{2}-8bc-16c^{2}. Consider -b^{2}-8bc-16c^{2} as a polynomial over variable b.

$$-b^{2}-8cb-16c^{2}$$

Find one factor of the form kb^{m}+n, where kb^{m} divides the monomial with the highest power -b^{2} and n divides the constant factor -16c^{2}. One such factor is b+4c. Factor the polynomial by dividing it by this factor.

$$\left(b+4c\right)\left(-b-4c\right)$$

Rewrite the complete factored expression.

$$5\left(b+4c\right)\left(-b-4c\right)$$

Evaluate

$$-5\left(b+4c\right)^{2}$$