Pascal’s Triangle and Binomial Expansion (Leaving Cert Mathematics): Quizzes

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Pascal’s Triangle and Binomial Expansion
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In Pascal's Triangle, what number begins and ends each row?

One

How is each interior number in Pascal's Triangle formed?

Sum of two numbers directly above it

What is one use of Pascal's Triangle?

Find coefficients in binomial expansion

Each row of Pascal's Triangle gives coefficients for which expression?

(a+b)n(a+b)^n

What is binomial expansion used for?

Expand expressions without full multiplication

In the general term (nr)xn−ryr\binom{n}{r}x^{n-r}y^r, what constraint applies to rr?

0≤r≤n0\le r \le n

In (a+b)n(a+b)^n, what must the powers of aa and bb in each term add up to?

nn

In (p+q)7(p+q)^7, if qq has power 5, what is the power of pp?

2

What value of rr corresponds to the sixth term in a binomial expansion?

5

What is the coefficient in the term (75)p2q5\binom{7}{5}p^2q^5?

21

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