Solve (a+b+2)(a+b-2)

$$( a + b + 2 ) ( a + b - 2 )$$

Evaluate

$$\left(a+b\right)^{2}-4$$

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=a+b and b=2.

$$\left(a+b\right)^{2}-2^{2}$$

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

$$a^{2}+2ab+b^{2}-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$a^{2}+2ab+b^{2}-4$$

Expand

$$a^{2}+2ab+b^{2}-4$$

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=a+b and b=2.

$$\left(a+b\right)^{2}-2^{2}$$

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

$$a^{2}+2ab+b^{2}-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$a^{2}+2ab+b^{2}-4$$