10 Questions
What is the Binomial Theorem used to expand?
(𝑎 + 𝑏)𝑛 when n is a positive integer
According to the binomial theorem, what is the expansion of (𝑎 + 𝑏)𝑛?
$𝐶𝑟 𝑏 𝑟 𝑎𝑛−𝑟$
What does the sum of the exponents of a and b in each term equal in the binomial expansion?
$n$
When should the infinite series be used to expand (𝑎 + 𝑏)𝑛 according to the definition?
When n is a negative integer
How many terms does the binomial expansion have according to the binomial theorem?
$n+1$
What is the expansion of (2𝑥 − 3𝑦)4?
(2𝑥)4 + 4𝐶1(−3𝑦)1(2𝑥)3 + 4𝐶2(−3𝑦)2(2𝑥)2 + 4𝐶3(−3𝑦)3(2𝑥)1 + (−3𝑦)4
What is the general term in the expansion of (𝑎 + 𝑏)^n, where 𝒓 = 0, 1, 2, … , 𝒏?
$T_{r+1} = nC_r b^r a^{n-r}$
Find the fourth term in the expansion of (𝑥 − 1)^9.
$-84x^6$
If n = 4, what are the orders of the middle terms in the expansion of (3𝑥 + 7𝑦)^8?
4, 6
Is there a term that does not contain 𝒙 (a constant term or a term free of 𝒙) in the expansion of (3𝑥 − 𝟐)^8?
$90720$
This quiz covers the concept of the Binomial Theorem, including its application in expanding expressions such as (a+b)^n and dealing with cases where the power is large. It also explains the definition of the Binomial Theorem and its application when n is a positive integer.
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