Solve (x+y)^2+4-4(x+y)

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

Evaluate

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

Solution Steps

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

$$x^{2}+2xy+y^{2}+4-4\left(x+y\right)$$

Use the distributive property to multiply -4 by x+y.

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

Expand

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

Solution Steps

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

$$x^{2}+2xy+y^{2}+4-4\left(x+y\right)$$

Use the distributive property to multiply -4 by x+y.

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