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# Coefficient

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Find the coefficient of y^4 in the expansion of (2y-7)^5.

May 4, 2022

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Using binomial theorem, $$\newcommand{\dsum}{\displaystyle\sum} (2y - 7)^5 = \dsum_{k = 0}^5 \binom{5}k (2y)^k (-7)^{5 -k}$$

To find the term in y^4, the power needs to be 4. So let k = 4:

$$\text{term in }y^4 = \displaystyle\binom{5}4 (2y)^4 (-7)^1 = -560y^4$$

Coefficient of y^4 = -560.

May 4, 2022