True or False? The binomial theorem only applies to linear expressions.

False. The binomial theorem applies to any two-term expression, but in IB it is most often applied to linear expressions.

True or False? Binomial coefficients are always integers .

True. Binomial coefficients are always integers .

True or False? In Pascal's triangle , each number is the sum of the two numbers directly above it.

True. In Pascal's triangle , each number is the sum of the two numbers directly above it.

What does the ellipsis (...) indicate in a binomial expansion?

The ellipsis (...) in a binomial expansion indicates that the expansion continues.

What does ' in ascending powers ' mean?

' In ascending powers ' means that the terms are arranged so that the power of the variable increases with each term.

IBMathsDPAnalysis & Approaches (AA)SLFlashcards1. Number & AlgebraBinomial Theorem

Binomial Theorem (DP IB Analysis & Approaches (AA))

Flashcards

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FrontBinomial Theorem
What is the binomial theorem?
FrontBinomial Theorem
State the equation for the binomial theorem.
BackBinomial Theorem
The equation for the binomial theorem is ${(a + b)}^{n} = a^{n} + {}^{n}{C_{1}} a^{n - 1} b + . . . + {}^{n}{C_{r}} a^{n - r} b^{r} + . . . + b^{n}$
Where:
${}^{n}{C_{r}} = \frac{n!}{r! (n - r)!}$
This equation is valid for any $n \in ℕ$ (i.e., $n = 0, 1, 2, 3, . . .$ ).
The equation is in the exam formula booklet.

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Cards in this collection (10)

What is the binomial theorem?
The binomial theorem is a method for expanding a two-term expression in a bracket raised to a power, e.g. ${(a + b)}^{n}$ .
True or False?
The binomial theorem only applies to linear expressions.
False.
The binomial theorem applies to any two-term expression, but in IB it is most often applied to linear expressions.
State the equation for the binomial theorem.
The equation for the binomial theorem is ${(a + b)}^{n} = a^{n} + {}^{n}{C_{1}} a^{n - 1} b + . . . + {}^{n}{C_{r}} a^{n - r} b^{r} + . . . + b^{n}$
Where:
- ${}^{n}{C_{r}} = \frac{n!}{r! (n - r)!}$
This equation is valid for any $n \in ℕ$ (i.e., $n = 0, 1, 2, 3, . . .$ ).
The equation is in the exam formula booklet.
What is the binomial coefficient?
The binomial coefficient ${}^{n}{C_{r}}$ is used to find the coefficients in a binomial expansion.
Its value is given by ${}^{n}{C_{r}} = \frac{n!}{r! (n - r)!}$ , which is in the exam formula booklet (although you will usually use your GDC to find the value of the coefficients in an expansion).
${}^{n}{C_{r}}$ also represents the number of ways to choose $r$ items out of $n$ different items.
True or False?
Binomial coefficients are always integers.
True.
Binomial coefficients are always integers.
True or False?
Pascal's triangle can be used to find binomial coefficients ${}^{n}{C_{r}}$ .
True.
Pascal's triangle is a triangular array of the binomial coefficients, and can be used to find ${}^{n}{C_{r}}$ for different values of $n$ and $r$ .
However Pascal's triangle becomes awkward to use when $n$ gets large.
True or False?
In Pascal's triangle, each number is the sum of the two numbers directly above it.
True.
In Pascal's triangle, each number is the sum of the two numbers directly above it.
True or False?
${}^{n}{C_{r}} = {}^{n}{C_{n - r}}$
True.
${}^{n}{C_{r}} = {}^{n}{C_{n - r}}$
E.g. ${}^{7}{C_{2}} = {}^{7}{C_{5}}$
What does the ellipsis (...) indicate in a binomial expansion?
The ellipsis (...) in a binomial expansion indicates that the expansion continues.
What does 'in ascending powers' mean?
'In ascending powers' means that the terms are arranged so that the power of the variable increases with each term.