Solve a^2+6ab-7b^2

$$a ^ { 2 } + 6 a b - 7 b ^ { 2 }$$

Factor

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

Solution Steps

Consider a^{2}+6ab-7b^{2} as a polynomial over variable a.

$$a^{2}+6ba-7b^{2}$$

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

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

Evaluate

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