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

$$( a - 2 b - 1 ) ( a - 2 b + 1 )$$

Evaluate

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

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=a-2b and b=1.

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

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

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

Calculate 1 to the power of 2 and get 1.

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

Expand

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

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=a-2b and b=1.

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

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

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

Calculate 1 to the power of 2 and get 1.

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