Solve a^2-12ab+35b^2

$$a ^ { 2 } - 12 a b + 35 b ^ { 2 }$$

Factor

$$\left(a-5b\right)\left(a-7b\right)$$

Solution Steps

Consider a^{2}-12ab+35b^{2} as a polynomial over variable a.

$$a^{2}-12ba+35b^{2}$$

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 35b^{2}. One such factor is a-7b. Factor the polynomial by dividing it by this factor.

$$\left(a-7b\right)\left(a-5b\right)$$

Evaluate

$$\left(a-5b\right)\left(a-7b\right)$$