Solve (m-2n+1)(m-2n-1)

$$( m - 2 n + 1 ) ( m - 2 n - 1 )$$

Evaluate

$$\left(m-2n\right)^{2}-1$$

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=m-2n and b=1.

$$\left(m-2n\right)^{2}-1^{2}$$

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

$$m^{2}-4mn+4n^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$m^{2}-4mn+4n^{2}-1$$

Expand

$$m^{2}-4mn+4n^{2}-1$$

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=m-2n and b=1.

$$\left(m-2n\right)^{2}-1^{2}$$

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

$$m^{2}-4mn+4n^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$m^{2}-4mn+4n^{2}-1$$