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The coefficient of a4b3c2d in the expansion of (a – b + c – d)10 is
- a)12600
- b)16200
- c)21600
- d)26100
Correct answer is option 'A'. Can you explain this answer?
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The coefficient of a4b3c2d in the expansion of (a – b + c &ndash...
Coefficient of a4b3c2d 
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The coefficient of a4b3c2d in the expansion of (a – b + c &ndash...
Expansion of (a – b + c – d)10
To find the coefficient of a⁴b³c²d in the expansion of (a – b + c – d)¹⁰, we can use the binomial theorem.
Binomial Theorem
The binomial theorem states that for any non-negative integer n:
(a + b)ⁿ = C(n, 0)aⁿb⁰ + C(n, 1)aⁿ⁻¹b¹ + C(n, 2)aⁿ⁻²b² + ... + C(n, n)a⁰bⁿ
where C(n, r) represents the binomial coefficient "n choose r".
Finding the Coefficient
In this case, we are interested in the term containing a⁴b³c²d, which corresponds to choosing a⁴ from a, b³ from -b, c² from c, and d from -d.
C(10, 4) * (-1)³ * (-1)² = 210 * (-1)³ * (-1)² = 210 * (-1) * 1 = -210
Therefore, the coefficient of a⁴b³c²d in the expansion of (a – b + c – d)¹⁰ is -210.
Final Answer
The correct answer is not provided in the options given.
To find the coefficient of a⁴b³c²d in the expansion of (a – b + c – d)¹⁰, we can use the binomial theorem.
Binomial Theorem
The binomial theorem states that for any non-negative integer n:
(a + b)ⁿ = C(n, 0)aⁿb⁰ + C(n, 1)aⁿ⁻¹b¹ + C(n, 2)aⁿ⁻²b² + ... + C(n, n)a⁰bⁿ
where C(n, r) represents the binomial coefficient "n choose r".
Finding the Coefficient
In this case, we are interested in the term containing a⁴b³c²d, which corresponds to choosing a⁴ from a, b³ from -b, c² from c, and d from -d.
C(10, 4) * (-1)³ * (-1)² = 210 * (-1)³ * (-1)² = 210 * (-1) * 1 = -210
Therefore, the coefficient of a⁴b³c²d in the expansion of (a – b + c – d)¹⁰ is -210.
Final Answer
The correct answer is not provided in the options given.
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