In the expansion of \((ab+bc+ca)^{12}\) find the coefficient of \({a}^{9}{b}^{11}c^{4}\)

Guest Mar 11, 2019

#4**+1 **

We can write this as

[ b(a + c) + ca ] ^{12}

We have .....

C( 12, 1) * [ b ( a + c)]^{11} * (ca)^{1} =

(12)b^{11} * (a + c)^{11} * a^{1} c^{1} =

(12)acb^{11} * (a + c)^{11} =

(12)acb^{11} * C(11,3) (a)^{8} * c^{3} =

(12) acb^{11} * (165)a^{8} c^{3} =

1980 a^{9} b^{11} c^{4}

^{ }

CPhill Mar 11, 2019