Solve (x+y-2)(x+y+2)

$$( x + y - 2 ) ( x + y + 2 )$$

Evaluate

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

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=x+y and b=2.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$x^{2}+2xy+y^{2}-4$$

Expand

$$x^{2}+2xy+y^{2}-4$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=x+y and b=2.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$x^{2}+2xy+y^{2}-4$$