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

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-9\right)^{2}.

$$x^{2}-18x+81+\left(y+6\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+6\right)^{2}.

$$x^{2}-18x+81+y^{2}+12y+36$$

Add 81 and 36 to get 117.

$$x^{2}-18x+117+y^{2}+12y$$

Expand

$$x^{2}-18x+y^{2}+12y+117$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-9\right)^{2}.

$$x^{2}-18x+81+\left(y+6\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+6\right)^{2}.

$$x^{2}-18x+81+y^{2}+12y+36$$

Add 81 and 36 to get 117.

$$x^{2}-18x+117+y^{2}+12y$$