Solve (x+y)^2+25-10(x+y)

$$( x + y ) ^ { 2 } + 25 - 10 ( x + y )$$

Evaluate

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

Solution Steps

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

$$x^{2}+2xy+y^{2}+25-10\left(x+y\right)$$

Use the distributive property to multiply -10 by x+y.

$$x^{2}+2xy+y^{2}+25-10x-10y$$

Expand

$$x^{2}+2xy-10x+y^{2}-10y+25$$

Solution Steps

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

$$x^{2}+2xy+y^{2}+25-10\left(x+y\right)$$

Use the distributive property to multiply -10 by x+y.

$$x^{2}+2xy+y^{2}+25-10x-10y$$