Solve (7x^2-xy+y^2)+(-x^2-9xy+3y^2)

$$( 7 x ^ { 2 } - x y + y ^ { 2 } ) + ( - x ^ { 2 } - 9 x y + 3 y ^ { 2 } )$$

Evaluate

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

Solution Steps

Combine -xy and -9xy to get -10xy.

$$7x^{2}-10xy+y^{2}-x^{2}+3y^{2}$$

Combine y^{2} and 3y^{2} to get 4y^{2}.

$$7x^{2}-10xy+4y^{2}-x^{2}$$

Combine 7x^{2} and -x^{2} to get 6x^{2}.

$$6x^{2}-10xy+4y^{2}$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$6x^{2}-10xy+4y^{2}$$

Factor out 2.

$$2\left(3x^{2}-5xy+2y^{2}\right)$$

Consider 3x^{2}-5xy+2y^{2}. Consider 3x^{2}-5xy+2y^{2} as a polynomial over variable x.

$$3x^{2}-5yx+2y^{2}$$

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

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

Rewrite the complete factored expression.

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