- The extension to
**multinomials**forms part of the theory of factors (ï¿½ 51). - (v.) When we have to multiply two
**multinomials**arranged according to powers of x, the method of detached coefficients enables us to omit the powers of x during the multiplication. - Continuing to develop the successive powers of A+a into
**multinomials**, we find that (A+a)3=A3+3A2a+3Aa2+a3, &c.; each power containing one more term than the preceding power, and the coefficients, when the terms are arranged in descending powers of A, being given by the following table I I ' 'I 2 I 1 3 3 I 4 6 4 I 5 IO to 5 I I x 6 15 20 15 6 &c., where the first line stands for (A+a)°=1. - (vi.) It follows that, if two
**multinomials**of the nth degree in x have equal values for more than n values of x, the corresponding coefficients are equal, so that the**multinomials**are equal for all values of x. - (iii.) Another result is that we can equate coefficients of like powers of x in two
**multinomials**obtained from the same expression by different methods of expansion.

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