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If the expansion of (x + y)^n contains a term with x^4y^3, what can be inferred
If the expansion of (x + y)^n contains a term with x^4y^3, what can be inferred about n?
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Q1
If the expansion of (x + y)^n contains a term with x^4y^3, what can be inferred about n?
n must be 7.
n must be greater than 7.
n must be less than 7.
n can be any integer.
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The sum of the exponents in the term x^4y^3 is 4 + 3 = 7, hence n must be 7.
Questions & Step-by-step Solutions
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Q
Q: If the expansion of (x + y)^n contains a term with x^4y^3, what can be inferred about n?
Solution:
The sum of the exponents in the term x^4y^3 is 4 + 3 = 7, hence n must be 7.
Steps: 5
Show Steps
Step 1: Identify the term given in the question, which is x^4y^3.
Step 2: Look at the exponents of x and y in the term. The exponent of x is 4 and the exponent of y is 3.
Step 3: Add the exponents together: 4 (from x) + 3 (from y) = 7.
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 7, we can conclude that n must be 7.
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