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If the expansion of (x + y)^n contains a term with x^4y^2, what can be inferred
If the expansion of (x + y)^n contains a term with x^4y^2, what can be inferred about the value of n?
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Q1
If the expansion of (x + y)^n contains a term with x^4y^2, what can be inferred about the value of n?
n must be 6.
n must be greater than 6.
n must be less than 6.
n can be any integer.
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In the term x^4y^2, the sum of the exponents (4 + 2) must equal n, hence n = 6.
Questions & Step-by-step Solutions
1 item
Q
Q: If the expansion of (x + y)^n contains a term with x^4y^2, what can be inferred about the value of n?
Solution:
In the term x^4y^2, the sum of the exponents (4 + 2) must equal n, hence n = 6.
Steps: 5
Show Steps
Step 1: Identify the term given in the question, which is x^4y^2.
Step 2: Look at the exponents in the term. The exponent of x is 4 and the exponent of y is 2.
Step 3: Add the exponents together: 4 (from x) + 2 (from y) = 6.
Step 4: Understand that in the expansion of (x + y)^n, the sum of the exponents in any term must equal n.
Step 5: Since the sum of the exponents is 6, we can conclude that n must be equal to 6.
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