Solve 7x^2+21xy-4xy-12y^2

$$7 x ^ { 2 } + 21 x y - 4 x y - 12 y ^ { 2 }$$

Factor

$$\left(7x-4y\right)\left(x+3y\right)$$

Solution Steps

Multiply and combine like terms.

$$7x^{2}+17xy-12y^{2}$$

Consider 7x^{2}+17xy-12y^{2} as a polynomial over variable x.

$$7x^{2}+17yx-12y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 7x^{2} and n divides the constant factor -12y^{2}. One such factor is 7x-4y. Factor the polynomial by dividing it by this factor.

$$\left(7x-4y\right)\left(x+3y\right)$$

Evaluate

$$\left(7x-4y\right)\left(x+3y\right)$$

Solution Steps

Combine 21xy and -4xy to get 17xy.

$$7x^{2}+17xy-12y^{2}$$