Binomial Theorem Mastery: Grade 12
This worksheet covers key concepts and applications of the Binomial Theorem for Grade 12 students, including expansion, identifying specific terms, and solving related problems.
Includes
Standards
Topics
Binomial Theorem Mastery
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Read each question carefully and provide clear, detailed solutions. Show all your work for full credit. You may use a calculator for calculations, but all steps for binomial expansion must be shown.
1. Expand the following binomial expression using the Binomial Theorem:
$(2x + 3y)^4$
2. For the expansion of $(x - 2)^5$, the coefficient of the $x^3$ term is .
3. The third term in the expansion of $(a + b)^6$ is .
4. The number of terms in the expansion of $(a+b)^n$ is $n$.
True
False
5. The sum of the exponents in each term of a binomial expansion $(a+b)^n$ is always $n$.
True
False
6. What is the coefficient of $x^2y^3$ in the expansion of $(x + y)^5$?
5
10
15
20
7. Which of the following is the general term in the expansion of $(a+b)^n$?
$C(n, r) a^{n-r} b^r$
$C(n, r) a^r b^{n-r}$
$n! / r! (n-r)! a^{n-r} b^r$
$ (a+b)^n $
8. Find the term independent of $x$ in the expansion of $(x^2 + \frac{1}{x})^{9}$.