Binomial Theorem & the Pascal's Triangle

Front

What is a binomial?

Back

A polynomial of the sum or difference of two terms.

Front

Which row of Pascal's Triangle would you use to expand (x+y)^3?

Back

1 3 3 1

Front

Expand: (a-b)^5

Back

a^5 - 5a^4b + 10a^3b^2 - 10a^2b^3 + 5ab^4 - b^5

Front

What is row 7 of Pascal's Triangle?

Back

1, 7, 21, 35, 35, 21, 7, 1

Front

What is the formula for the binomial expansion of (a+b)^n?

Back

Front

What does the binomial coefficient \( \binom{n}{k} \) represent?

Back

The number of ways to choose k elements from a set of n elements.

Front

What is the relationship between Pascal's Triangle and binomial coefficients?

Back

Each entry in Pascal's Triangle is a binomial coefficient, representing the coefficients in the expansion of (a+b)^n.

Front

How do you find the coefficients for (x+y)^4 using Pascal's Triangle?

Back

Use row 4 of Pascal's Triangle: 1, 4, 6, 4, 1.

Front

What is the value of \( \binom{5}{2} \)?

Back

10

Front

Expand: (2x + 3)^3

Back

8x^3 + 36x^2 + 54x + 27