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

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

Expand

$$x^{2}-10x+y^{2}-10y+50$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$x^{2}-10x+25+\left(y-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-5\right)^{2}.

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

Add 25 and 25 to get 50.

$$x^{2}-10x+50+y^{2}-10y$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$x^{2}-10x+25+\left(y-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-5\right)^{2}.

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

Add 25 and 25 to get 50.

$$x^{2}-10x+50+y^{2}-10y$$