First slide

Binomial theorem for positive integral Index

Question

The sum of the coefficients in the binomial expansion ${(a - x)}^{5}$

Very Easy

A

0
B

10
C

12
D

32

Solution

${(a - x)}^{n} = {}^{n}C_{0} a^{n} x^{0} - {}^{n}C_{1} a^{n - 1} x^{1} + {}^{n}C_{2} a^{n - 2} x^{2} - ........ + {(- 1)}^{n} {}^{n}C_{n} a^{0} x^{n} ∴ {(a - x)}^{5} = {}^{5}C_{0} a^{5} x^{0} - {}^{5}C_{1} a^{4} x^{1} + {}^{5}C_{2} a^{3} x^{2} - {}^{5}C_{3} a^{2} x^{3} + {}^{5}C_{4} a^{1} x^{4} - {}^{5}C_{5} a^{0} x^{5} = a^{5} - 5 a^{4} x + 10 a^{3} x^{2} - 10 a^{2} x^{3} + 5 a x^{4} - x^{5} A c c o r d i n g t o p r o b l e m s u m o f c o e f f i c i e n t s a r e 1 - 5 + 10 - 10 + 5 - 1 = 0$

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