Solve left(x-3right)^2+left(y-2right)^2

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

Expand

$$x^{2}-6x+y^{2}-4y+13$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

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

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

$$x^{2}-6x+9+y^{2}-4y+4$$

Add 9 and 4 to get 13.

$$x^{2}-6x+13+y^{2}-4y$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

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

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

$$x^{2}-6x+9+y^{2}-4y+4$$

Add 9 and 4 to get 13.

$$x^{2}-6x+13+y^{2}-4y$$