Solve 12x^2-20xy-9xy+15y^2

$$12 x ^ { 2 } - 20 x y - 9 x y + 15 y ^ { 2 }$$

Factor

$$\left(3x-5y\right)\left(4x-3y\right)$$

Solution Steps

Multiply and combine like terms.

$$12x^{2}-29xy+15y^{2}$$

Consider 12x^{2}-29xy+15y^{2} as a polynomial over variable x.

$$12x^{2}-29yx+15y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 12x^{2} and n divides the constant factor 15y^{2}. One such factor is 3x-5y. Factor the polynomial by dividing it by this factor.

$$\left(3x-5y\right)\left(4x-3y\right)$$

Evaluate

$$\left(3x-5y\right)\left(4x-3y\right)$$

Solution Steps

Combine -20xy and -9xy to get -29xy.

$$12x^{2}-29xy+15y^{2}$$