Alg10.8

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Find the coefficient of x^3\, in the expansion of (3x+4)^6\,

To find the coefficient of x^3\, we have to find T_{3+1}=6\!C_3 \cdot (3x)^{6-3}\cdot 4^3\,

6\!C_3 \cdot 3^3 \cdot x^3 \cdot 64\,

6\!C_3 \cdot 27 \cdot 64 \cdot x^3\,

Therefore,the coefficient of x^3\, is 6\!C_3 \cdot 3^3\cdot 4^3\,

By expanding the coefficient,we get \frac{(6!)}{(6-3)!3!}\cdot 27 \cdot 256=5\cdot 4\cdot 27 \cdot 64=5 (2^2) (3^3) (2^6)=5\cdot(2^8)\cdot (3^3)\,


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