Solve 3a^2-19ab+28b^2

$$3 a ^ { 2 } - 19 a b + 28 b ^ { 2 }$$

Factor

$$\left(a-4b\right)\left(3a-7b\right)$$

Solution Steps

Consider 3a^{2}-19ab+28b^{2} as a polynomial over variable a.

$$3a^{2}-19ba+28b^{2}$$

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 3a^{2} and n divides the constant factor 28b^{2}. One such factor is 3a-7b. Factor the polynomial by dividing it by this factor.

$$\left(3a-7b\right)\left(a-4b\right)$$

Evaluate

$$\left(a-4b\right)\left(3a-7b\right)$$