Consider , where and are nonzero constants.

Expand this binomial expression.

Binomial expansion: .

.

The two middle terms in the expansion are and .

These terms will be equal only if .

Therefore, the two middle terms of the expansion sometimes have the same coefficients, If the coefficients of each term in the binomial are equal, then two middle terms of the expansion will have the same coefficients.

The statement is sometimes true. \ \