Solve -49a^3-14a^2b-ab^2

$$- 49 a ^ { 3 } - 14 a ^ { 2 } b - a b ^ { 2 }$$

Factor

$$-a\left(7a+b\right)^{2}$$

Solution Steps

Factor out a.

$$a\left(-49a^{2}-14ab-b^{2}\right)$$

Consider -49a^{2}-14ab-b^{2}. Consider -49a^{2}-14ab-b^{2} as a polynomial over variable a.

$$-49a^{2}-14ba-b^{2}$$

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power -49a^{2} and n divides the constant factor -b^{2}. One such factor is 7a+b. Factor the polynomial by dividing it by this factor.

$$\left(7a+b\right)\left(-7a-b\right)$$

Rewrite the complete factored expression.

$$a\left(7a+b\right)\left(-7a-b\right)$$

Evaluate

$$-a\left(7a+b\right)^{2}$$