Solve 6x^2+24xy-3xy-12y^2

$$6 x ^ { 2 } + 24 x y - 3 x y - 12 y ^ { 2 }$$

Factor

$$3\left(2x-y\right)\left(x+4y\right)$$

Solution Steps

Factor out 3.

$$3\left(2x^{2}+8xy-xy-4y^{2}\right)$$

Consider 2x^{2}+8xy-xy-4y^{2}. Multiply and combine like terms.

$$2x^{2}+7xy-4y^{2}$$

Consider 2x^{2}+7xy-4y^{2}. Consider 2x^{2}+7xy-4y^{2} as a polynomial over variable x.

$$2x^{2}+7yx-4y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 2x^{2} and n divides the constant factor -4y^{2}. One such factor is 2x-y. Factor the polynomial by dividing it by this factor.

$$\left(2x-y\right)\left(x+4y\right)$$

Rewrite the complete factored expression.

$$3\left(2x-y\right)\left(x+4y\right)$$

Evaluate

$$3\left(2x-y\right)\left(x+4y\right)$$

Solution Steps

Combine 24xy and -3xy to get 21xy.

$$6x^{2}+21xy-12y^{2}$$