The Binomial Theorem (VCE SSCE Mathematical Methods): Quizzes

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The Binomial Theorem
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What is a binomial expression?

An expression with two terms

How many terms are in the expansion of (x+b)n(x + b)^n?

n+1n + 1 terms

In Pascal's triangle, how is each number formed?

Sum of two numbers directly above it

What is the formula for (nr)\binom{n}{r}?

n!r!(nr)!\frac{n!}{r!(n-r)!}

What is the value of 5!5!?

120120

To find the 8th term in a binomial expansion, which value of rr should be used?

r=7r = 7

In each term of (x+b)n(x + b)^n, what does the sum of the powers of xx and bb equal?

nn

How are binomial expansions written by convention?

With decreasing powers of xx

As we move left to right in (x+b)n(x + b)^n, what happens to the powers of xx?

They decrease from nn to 00

What is the general formula for (x+b)n(x + b)^n using summation notation?

k=0n(nk)xnkbk\sum_{k=0}^{n} \binom{n}{k} x^{n-k} b^k

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