Solve (5x^2-xy+y^2)+(-x^2-6xy+2y^2)

$$( 5 x ^ { 2 } - x y + y ^ { 2 } ) + ( - x ^ { 2 } - 6 x y + 2 y ^ { 2 } )$$

Evaluate

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

Solution Steps

Combine -xy and -6xy to get -7xy.

$$5x^{2}-7xy+y^{2}-x^{2}+2y^{2}$$

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

$$5x^{2}-7xy+3y^{2}-x^{2}$$

Combine 5x^{2} and -x^{2} to get 4x^{2}.

$$4x^{2}-7xy+3y^{2}$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$4x^{2}-7xy+3y^{2}$$

Consider 4x^{2}-7xy+3y^{2} as a polynomial over variable x.

$$4x^{2}-7yx+3y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 4x^{2} and n divides the constant factor 3y^{2}. One such factor is 4x-3y. Factor the polynomial by dividing it by this factor.

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