Solve 2a^2-30ab+112b^2

$$2 a ^ { 2 } - 30 a b + 112 b ^ { 2 }$$

Factor

$$2\left(a-7b\right)\left(a-8b\right)$$

Solution Steps

Factor out 2.

$$2\left(a^{2}-15ab+56b^{2}\right)$$

Consider a^{2}-15ab+56b^{2}. Consider a^{2}-15ab+56b^{2} as a polynomial over variable a.

$$a^{2}-15ba+56b^{2}$$

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 56b^{2}. One such factor is a-8b. Factor the polynomial by dividing it by this factor.

$$\left(a-8b\right)\left(a-7b\right)$$

Rewrite the complete factored expression.

$$2\left(a-8b\right)\left(a-7b\right)$$

Evaluate

$$2\left(a-7b\right)\left(a-8b\right)$$