Binomial Expansion Worksheet
Grade 12 math worksheet on binomial expansion, covering the binomial theorem, Pascal's triangle, and finding specific terms.
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Binomial Expansion Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. The coefficients of the binomial expansion \((a+b)^n\) can be found using .
2. The Binomial Theorem states that for any positive integer \(n\), the expansion of \((x+y)^n\) is given by \(\sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k\), where \(\binom{n}{k}\) is the coefficient.
3. Expand \((2x + 3y)^3\) using the binomial theorem.
4. What is the coefficient of the \(x^2y^3\) term in the expansion of \((x+y)^5\)?
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25
5. Find the 4th term in the expansion of \((x - 2)^7\).
6. The sum of the exponents in each term of a binomial expansion \((a+b)^n\) is always equal to \(n\).
True
False
7. Find the term independent of \(x\) in the expansion of \((x^2 + \frac{1}{x})^9\).