Now, when _(x+y)ᴹ_ is multiplied by _x+y_ to give _(x+y)ᴹ⁺¹_, we multiply
first by _x_ and then by _y_ instead of by _x_ and add the two results.
When we multiply by _x_, the second of the above three terms will be the
only one giving a term involving _xᵖy𐞥⁺¹_ and the third will be the only
one giving a term in _xᵖ⁻¹y𐞥⁺²_; and when we multiply by _y_ the first
will be the only term giving a term in _xᵖy𐞥⁺¹_, and the second will be
the only term giving a term in _xᵖ⁻¹y𐞥⁺²_. Hence, adding like terms,
we find that the coefficient of _xᵖy𐞥⁺¹_in the expansion of _(x+y)ᴹ⁺¹_
will be the sum of the coefficients of the first two of the above three
terms, and that the coefficient of _xᵖ⁻¹y𐞥⁺²_ will be the sum of the
coefficients of the last two terms. Hence, two successive terms in the
expansion of _(x+y)ᴹ⁺¹_ will be