find the specified term in the expansion in the following binomials

fifth term of (2a+3b)^12. evaluate it when a=1/3 b=1/4

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find the specified term in the expansion in the following
binomials
fifth term of (2a+3b)^12 evaluate it when a=1/3 b=1/4

Aakash Sharma · Accepted Answer

The specified term in the expansion of (x + y)ⁿ is given by

$T_{r + 1} = {}^{n}{C_{r}} x^{n - r} y^{r}$

Putting x = 2a, y = 3b, n = 12 and r = 4 we get

$T_{5} = {}^{12}{C_{4}} {(2 a)}^{8} {(3 b)}^{4} = 495 \times 2^{8} a^{8} \times 3^{4} b^{4} = 2^{8} \times 3^{6} \times 5 \times 11 \times a^{8} \times b^{4} Now when a = \frac{1}{3}, b = \frac{1}{4} = \frac{1}{2^{2}}, we get T_{5} = 2^{8} \times 3^{6} \times 5 \times 11 \times (\frac{1}{3})^{8} \times (\frac{1}{2^{2}})^{4} = \frac{55}{9}$

find the specified term in the expansion in the following binomials fifth term of (2a+3b)^12. evaluate it when a=1/3 b=1/4

find the specified term in the expansion in the following binomials

fifth term of (2a+3b)^12. evaluate it when a=1/3 b=1/4