Solve left(x-yright)^2+6(x-y)+9

$${ \left(x-y \right) }^{ 2 } +6(x-y)+9$$

Evaluate

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

Solution Steps

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

$$x^{2}-2xy+y^{2}+6\left(x-y\right)+9$$

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

$$x^{2}-2xy+y^{2}+6x-6y+9$$

Expand

$$x^{2}-2xy+6x+y^{2}-6y+9$$

Solution Steps

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

$$x^{2}-2xy+y^{2}+6\left(x-y\right)+9$$

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

$$x^{2}-2xy+y^{2}+6x-6y+9$$