Solve (x+a)^2-2(x+a)(y+a)+(y+a)^2=

$$( x + a ) ^ { 2 } - 2 ( x + a ) ( y + a ) + ( y + a ) ^ { 2 } =$$

Evaluate

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

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(x+a\right)^{2}.

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

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(y+a\right)^{2}.

$$x^{2}+2xa+a^{2}-2\left(x+a\right)\left(y+a\right)+y^{2}+2ya+a^{2}$$

Use the distributive property to multiply -2 by x+a.

$$x^{2}+2xa+a^{2}+\left(-2x-2a\right)\left(y+a\right)+y^{2}+2ya+a^{2}$$

Use the distributive property to multiply -2x-2a by y+a.

$$x^{2}+2xa+a^{2}-2xy-2xa-2ay-2a^{2}+y^{2}+2ya+a^{2}$$

Combine 2xa and -2xa to get 0.

$$x^{2}+a^{2}-2xy-2ay-2a^{2}+y^{2}+2ya+a^{2}$$

Combine a^{2} and -2a^{2} to get -a^{2}.

$$x^{2}-a^{2}-2xy-2ay+y^{2}+2ya+a^{2}$$

Combine -2ay and 2ya to get 0.

$$x^{2}-a^{2}-2xy+y^{2}+a^{2}$$

Combine -a^{2} and a^{2} to get 0.

$$x^{2}-2xy+y^{2}$$

Expand

$$x^{2}-2xy+y^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(x+a\right)^{2}.

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

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(y+a\right)^{2}.

$$x^{2}+2xa+a^{2}-2\left(x+a\right)\left(y+a\right)+y^{2}+2ya+a^{2}$$

Use the distributive property to multiply -2 by x+a.

$$x^{2}+2xa+a^{2}+\left(-2x-2a\right)\left(y+a\right)+y^{2}+2ya+a^{2}$$

Use the distributive property to multiply -2x-2a by y+a.

$$x^{2}+2xa+a^{2}-2xy-2xa-2ay-2a^{2}+y^{2}+2ya+a^{2}$$

Combine 2xa and -2xa to get 0.

$$x^{2}+a^{2}-2xy-2ay-2a^{2}+y^{2}+2ya+a^{2}$$

Combine a^{2} and -2a^{2} to get -a^{2}.

$$x^{2}-a^{2}-2xy-2ay+y^{2}+2ya+a^{2}$$

Combine -2ay and 2ya to get 0.

$$x^{2}-a^{2}-2xy+y^{2}+a^{2}$$

Combine -a^{2} and a^{2} to get 0.

$$x^{2}-2xy+y^{2}$$