Solve (x_{y}+x+2)(x_{y}+x-2)

$$( x _ { y } + x + 2 ) ( x _ { y } + x - 2 )$$

Evaluate

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

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}+x and b=2.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Expand

$$x^{2}+2xx_{y}+x_{y}^{2}-4$$

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}+x and b=2.

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

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

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

Calculate 2 to the power of 2 and get 4.

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