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

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

Expand

$$m^{2}+2mt-4n^{2}+4n+t^{2}-1$$

Solution Steps

Apply the distributive property by multiplying each term of m-2n+t+1 by each term of m+2n+t-1.

$$m^{2}+2mn+mt-m-2nm-4n^{2}-2nt+2n+tm+2tn+t^{2}-t+m+2n+t-1$$

Combine 2mn and -2nm to get 0.

$$m^{2}+mt-m-4n^{2}-2nt+2n+tm+2tn+t^{2}-t+m+2n+t-1$$

Combine mt and tm to get 2mt.

$$m^{2}+2mt-m-4n^{2}-2nt+2n+2tn+t^{2}-t+m+2n+t-1$$

Combine -2nt and 2tn to get 0.

$$m^{2}+2mt-m-4n^{2}+2n+t^{2}-t+m+2n+t-1$$

Combine -m and m to get 0.

$$m^{2}+2mt-4n^{2}+2n+t^{2}-t+2n+t-1$$

Combine 2n and 2n to get 4n.

$$m^{2}+2mt-4n^{2}+4n+t^{2}-t+t-1$$

Combine -t and t to get 0.

$$m^{2}+2mt-4n^{2}+4n+t^{2}-1$$

Evaluate

$$\left(m-2n+t+1\right)\left(m+2n+t-1\right)$$

Solution Steps

Apply the distributive property by multiplying each term of m-2n+t+1 by each term of m+2n+t-1.

$$m^{2}+2mn+mt-m-2nm-4n^{2}-2nt+2n+tm+2tn+t^{2}-t+m+2n+t-1$$

Combine 2mn and -2nm to get 0.

$$m^{2}+mt-m-4n^{2}-2nt+2n+tm+2tn+t^{2}-t+m+2n+t-1$$

Combine mt and tm to get 2mt.

$$m^{2}+2mt-m-4n^{2}-2nt+2n+2tn+t^{2}-t+m+2n+t-1$$

Combine -2nt and 2tn to get 0.

$$m^{2}+2mt-m-4n^{2}+2n+t^{2}-t+m+2n+t-1$$

Combine -m and m to get 0.

$$m^{2}+2mt-4n^{2}+2n+t^{2}-t+2n+t-1$$

Combine 2n and 2n to get 4n.

$$m^{2}+2mt-4n^{2}+4n+t^{2}-t+t-1$$

Combine -t and t to get 0.

$$m^{2}+2mt-4n^{2}+4n+t^{2}-1$$