Solve -a^3-3a^2b-3ab^2-b^3

$$- a ^ { 3 } - 3 a ^ { 2 } b - 3 a b ^ { 2 } - b ^ { 3 }$$

Factor

$$-\left(a+b\right)^{3}$$

Solution Steps

Consider -a^{3}-3a^{2}b-3ab^{2}-b^{3} as a polynomial over variable a.

$$-a^{3}-3ba^{2}-3b^{2}a-b^{3}$$

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power -a^{3} and n divides the constant factor -b^{3}. One such factor is a+b. Factor the polynomial by dividing it by this factor.

$$\left(a+b\right)\left(-a^{2}-2ab-b^{2}\right)$$

Consider -a^{2}-2ab-b^{2}. Consider -a^{2}-2ab-b^{2} as a polynomial over variable a.

$$-a^{2}-2ba-b^{2}$$

Find one factor of the form pa^{q}+u, where pa^{q} divides the monomial with the highest power -a^{2} and u divides the constant factor -b^{2}. One such factor is a+b. Factor the polynomial by dividing it by this factor.

$$\left(a+b\right)\left(-a-b\right)$$

Rewrite the complete factored expression.

$$\left(-a-b\right)\left(a+b\right)^{2}$$

Evaluate

$$-\left(a+b\right)^{3}$$