Solve (x+11)^2+(y-5)^2-(x-y)

$$( x + 11 ) ^ { 2 } + ( y - 5 ) ^ { 2 } - ( x - y )$$

Evaluate

$$\left(x+11\right)^{2}+\left(y-5\right)^{2}+y-x$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+11\right)^{2}.

$$x^{2}+22x+121+\left(y-5\right)^{2}-\left(x-y\right)$$

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

$$x^{2}+22x+121+y^{2}-10y+25-\left(x-y\right)$$

Add 121 and 25 to get 146.

$$x^{2}+22x+146+y^{2}-10y-\left(x-y\right)$$

To find the opposite of x-y, find the opposite of each term.

$$x^{2}+22x+146+y^{2}-10y-x+y$$

Combine 22x and -x to get 21x.

$$x^{2}+21x+146+y^{2}-10y+y$$

Combine -10y and y to get -9y.

$$x^{2}+21x+146+y^{2}-9y$$

Expand

$$x^{2}+21x+y^{2}-9y+146$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+11\right)^{2}.

$$x^{2}+22x+121+\left(y-5\right)^{2}-\left(x-y\right)$$

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

$$x^{2}+22x+121+y^{2}-10y+25-\left(x-y\right)$$

Add 121 and 25 to get 146.

$$x^{2}+22x+146+y^{2}-10y-\left(x-y\right)$$

To find the opposite of x-y, find the opposite of each term.

$$x^{2}+22x+146+y^{2}-10y-x+y$$

Combine 22x and -x to get 21x.

$$x^{2}+21x+146+y^{2}-10y+y$$

Combine -10y and y to get -9y.

$$x^{2}+21x+146+y^{2}-9y$$