Solve left(x-3right)^2+left(y-4right)^2

$${ \left(x-3 \right) }^{ 2 } + { \left(y-4 \right) }^{ 2 }$$

Expand

$$x^{2}-6x+y^{2}-8y+25$$

Solution Steps

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

$$x^{2}-6x+9+\left(y-4\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-4\right)^{2}.

$$x^{2}-6x+9+y^{2}-8y+16$$

Add 9 and 16 to get 25.

$$x^{2}-6x+25+y^{2}-8y$$

Evaluate

$$\left(x-3\right)^{2}+\left(y-4\right)^{2}$$

Solution Steps

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

$$x^{2}-6x+9+\left(y-4\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-4\right)^{2}.

$$x^{2}-6x+9+y^{2}-8y+16$$

Add 9 and 16 to get 25.

$$x^{2}-6x+25+y^{2}-8y$$