Solve left(2a+2b+1right)left(2a+2b-1right)

$$\left( 2a+2b+1 \right) \left( 2a+2b-1 \right)$$

Evaluate

$$\left(2a+2b\right)^{2}-1$$

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=2a+2b and b=1.

$$\left(2a+2b\right)^{2}-1^{2}$$

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

$$4a^{2}+8ab+4b^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$4a^{2}+8ab+4b^{2}-1$$

Expand

$$4a^{2}+8ab+4b^{2}-1$$

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=2a+2b and b=1.

$$\left(2a+2b\right)^{2}-1^{2}$$

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

$$4a^{2}+8ab+4b^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$4a^{2}+8ab+4b^{2}-1$$