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What is the general term in the expansion of (2y-4x)44?
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
What is the general term in the expansion of (2y-4x)44?a)b)c)d)Correct...
n = 44, p = 2y q = -4x
General term of (p+q)n is given by
T(r+1) = nCr . pr . q(n-r)
= 44Cr . (2y)r . (-4x)(44-r)
General term of (p+q)n is given by
T(r+1) = nCr . pr . q(n-r)
= 44Cr . (2y)r . (-4x)(44-r)
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What is the general term in the expansion of (2y-4x)44?a)b)c)d)Correct...
The general term in the expansion of (2y-4x)^44 can be determined using the binomial theorem. The binomial theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a + b)^n can be written as:
(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn * a^0 * b^n
Where nCr represents the binomial coefficient and is calculated using the formula:
nCr = n! / (r! * (n-r)!)
Now let's apply the binomial theorem to the given expression.
The expansion of (2y-4x)^44 can be written as:
(2y)^44 * (-4x)^0 * 44C0 + (2y)^43 * (-4x)^1 * 44C1 + (2y)^42 * (-4x)^2 * 44C2 + ... + (2y)^0 * (-4x)^44 * 44C44
Simplifying further, we can write this as:
44C0 * (2y)^44 * (-4x)^0 + 44C1 * (2y)^43 * (-4x)^1 + 44C2 * (2y)^42 * (-4x)^2 + ... + 44C44 * (2y)^0 * (-4x)^44
Now let's compare this with the given options:
a) 44Cr * (2y)^r * (-4x)^(44-r)
Comparing the terms, we can see that this option matches with the expansion of (2y-4x)^44.
Therefore, the correct answer is option 'A'.
(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn * a^0 * b^n
Where nCr represents the binomial coefficient and is calculated using the formula:
nCr = n! / (r! * (n-r)!)
Now let's apply the binomial theorem to the given expression.
The expansion of (2y-4x)^44 can be written as:
(2y)^44 * (-4x)^0 * 44C0 + (2y)^43 * (-4x)^1 * 44C1 + (2y)^42 * (-4x)^2 * 44C2 + ... + (2y)^0 * (-4x)^44 * 44C44
Simplifying further, we can write this as:
44C0 * (2y)^44 * (-4x)^0 + 44C1 * (2y)^43 * (-4x)^1 + 44C2 * (2y)^42 * (-4x)^2 + ... + 44C44 * (2y)^0 * (-4x)^44
Now let's compare this with the given options:
a) 44Cr * (2y)^r * (-4x)^(44-r)
Comparing the terms, we can see that this option matches with the expansion of (2y-4x)^44.
Therefore, the correct answer is option 'A'.
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What is the general term in the expansion of (2y-4x)44?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What is the general term in the expansion of (2y-4x)44?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the general term in the expansion of (2y-4x)44?a)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
What is the general term in the expansion of (2y-4x)44?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What is the general term in the expansion of (2y-4x)44?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the general term in the expansion of (2y-4x)44?a)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
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