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If the expansion of (x + y)^n contains a term with x^4y^3, what can be inferred

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Question: If the expansion of (x + y)^n contains a term with x^4y^3, what can be inferred about n?

Options:

  1. n must be 7.
  2. n must be greater than 7.
  3. n must be less than 7.
  4. n can be any integer.

Correct Answer: n must be 7.

Solution: 

The sum of the exponents in the term x^4y^3 is 4 + 3 = 7, hence n must be 7.

If the expansion of (x + y)^n contains a term with x^4y^3, what can be inferred

Practice Questions

Q1
If the expansion of (x + y)^n contains a term with x^4y^3, what can be inferred about n?
  1. n must be 7.
  2. n must be greater than 7.
  3. n must be less than 7.
  4. n can be any integer.

Questions & Step-by-Step Solutions

If the expansion of (x + y)^n contains a term with x^4y^3, what can be inferred about n?
  • 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.
  • Binomial Expansion – Understanding how to expand expressions of the form (x + y)^n and identify the coefficients and terms.
  • Exponents in Terms – Recognizing that the sum of the exponents in a term from the binomial expansion must equal n.
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