Solve 6(x+y)^2-1-2(x+y)^2

$$6 ( x + y ) ^ { 2 - 1 } - 2 ( x + y ) ^ { 2 }$$

Evaluate

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

Solution Steps

Subtract 1 from 2 to get 1.

$$6\left(x+y\right)^{1}-2\left(x+y\right)^{2}$$

Calculate x+y to the power of 1 and get x+y.

$$6\left(x+y\right)-2\left(x+y\right)^{2}$$

Use the distributive property to multiply 6 by x+y.

$$6x+6y-2\left(x+y\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.

$$6x+6y-2\left(x^{2}+2xy+y^{2}\right)$$

Use the distributive property to multiply -2 by x^{2}+2xy+y^{2}.

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

Factor

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

Solution Steps

Subtract 1 from 2 to get 1.

$$factor(6\left(x+y\right)^{1}-2\left(x+y\right)^{2})$$

Calculate x+y to the power of 1 and get x+y.

$$factor(6\left(x+y\right)-2\left(x+y\right)^{2})$$

Use the distributive property to multiply 6 by x+y.

$$factor(6x+6y-2\left(x+y\right)^{2})$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.

$$factor(6x+6y-2\left(x^{2}+2xy+y^{2}\right))$$

Use the distributive property to multiply -2 by x^{2}+2xy+y^{2}.

$$factor(6x+6y-2x^{2}-4xy-2y^{2})$$

Factor out 2.

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

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

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

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

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

Rewrite the complete factored expression.

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