Solve {l}{3a^2-8ab}{+4b^2}

$$\left. \begin{array} { l } { 3 a ^ { 2 } - 8 a b } \\ { + 4 b ^ { 2 } } \end{array} \right.$$

Factor

$$\left(a-2b\right)\left(3a-2b\right)$$

Solution Steps

Consider 3a^{2}-8ab+4b^{2} as a polynomial over variable a.

$$3a^{2}-8ba+4b^{2}$$

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 4b^{2}. One such factor is 3a-2b. Factor the polynomial by dividing it by this factor.

$$\left(3a-2b\right)\left(a-2b\right)$$

Evaluate

$$\left(a-2b\right)\left(3a-2b\right)$$