Solve 6a^2-9ax-2ax+3x^2=

$$6 a ^ { 2 } - 9 a x - 2 a x + 3 x ^ { 2 } =$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$3x^{2}-11ax+6a^{2}$$

Consider 3x^{2}-11ax+6a^{2} as a polynomial over variable a.

$$6a^{2}-11xa+3x^{2}$$

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 6a^{2} and n divides the constant factor 3x^{2}. One such factor is -3x+2a. Factor the polynomial by dividing it by this factor.

$$\left(-3x+2a\right)\left(-x+3a\right)$$

Evaluate

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

Solution Steps

Combine -9ax and -2ax to get -11ax.

$$6a^{2}-11ax+3x^{2}$$