Basic Concepts
The number of terms in the expansion of (a+b)n(a+b)n.
What is n+1n+1?
The third row of Pascal’s Triangle is this.
What is 1, 2, 1?
The general term of (a+b)n(a+b)n is given by this formula.
What is (nk)an−kbk(kn)an−kbk?
Expand (x+1)2(x+1)2.
What is x2+2x+1x2+2x+1?
Binomial expansion is used in this school subject.
What is math?
The name of the two terms being added in a binomial.
What are the binomial terms?
This triangle gives the coefficients of binomial expansions.
What is Pascal’s Triangle?
This symbol (nk)(kn) stands for this operation.
What is "n choose k" or a binomial coefficient?
The middle term in (x+2)4(x+2)4
What is 6x2⋅4=96x26x2⋅4=96x2?
You can use binomial expansion to help figure out how money grows over time in a bank.
What is interest?
The coefficient of the first term in any binomial expansion.
What is 1?
The fifth row corresponds to this binomial power.
What is (a+b)4(a+b)4?
The number of terms in (x+2)3(x+2)3.
What is 4?
The constant term in (2x−3)3(2x−3)3.
What is −27−27?
Binomials can help find the chance of something happening.
What is probability?
In (x+y)n(x+y)n, this represents the number of times the binomial is multiplied.
What is the exponent nn?
The sum of the numbers in the nnth row of Pascal’s Triangle.
What is 2n2n?
The expansion of (x−y)3(x−y)3 includes this many negative terms.
What is 2?
Expand (a−b)2(a−b)2.
What is a2−2ab+b2a2−2ab+b2?
What subject uses binomial expansion to help figure out how many ways things can be true or false?
What is logic?
The expression (a+b)2(a+b)2 expands to this.
What is a2+2ab+b2a2+2ab+b2?
The binomial coefficients are also known by this combinatorial term.
What are combinations or "n choose k"?
(2x+3)4, find the third term (when k = 2).
What is (42)(2x)2(3)2=6(4x2)(9)=216x2(24)(2x)2(3)2=6(4x2)(9)=216x2?
Find the coefficient of x3x3 in (x+2)5(x+2)5.
What is (53)x3(2)2=10⋅4=40(35)x3(2)2=10⋅4=40?
You can use binomial expansion to guess how many times something will happen, like flipping a coin.
What is outcomes or chances?