Solve (x+y+4)(x+y-4)

$$( x + y + 4 ) ( x + y - 4 )$$

Evaluate

$$\left(x+y\right)^{2}-16$$

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=4.

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

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

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

Calculate 4 to the power of 2 and get 16.

$$x^{2}+2xy+y^{2}-16$$

Expand

$$x^{2}+2xy+y^{2}-16$$

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=4.

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

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

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

Calculate 4 to the power of 2 and get 16.

$$x^{2}+2xy+y^{2}-16$$