2H1 The Binomial Theorem - classwork

Front

What is the Binomial Theorem?

Back

The Binomial Theorem provides a formula for expanding expressions of the form (a + b)^n, where n is a non-negative integer.

Front

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

Back

The number of terms in the binomial expansion of (a + b)^n is n + 1.

Front

What does Pascal's Triangle represent in relation to the Binomial Theorem?

Back

Pascal's Triangle represents the coefficients of the expanded form of (a + b)^n.

Front

What is the 0th row of Pascal's Triangle?

Back

The 0th row of Pascal's Triangle is simply 1.

Front

What is the formula for the coefficients in the Binomial Theorem?

Back

The coefficients in the Binomial Theorem are given by the binomial coefficients, which can be calculated using the formula C(n, k) = n! / (k!(n-k)!), where n is the degree and k is the term number.

Front

What is the 11th row of Pascal's Triangle?

Back

The 11th row of Pascal's Triangle is 1, 11, 55, 165, 462, 924, 462, 165, 55, 11, 1.

Front

How do you find the fourth term in the expansion of (a + b)^8?

Back

The fourth term can be found using the formula T(k+1) = C(n, k) * a^(n-k) * b^k, where n=8 and k=3. The coefficient is C(8, 3) = 56.

Front

What is the significance of the 23rd row in Pascal's Triangle?

Back

The 23rd row in Pascal's Triangle provides the coefficients for the expansion of (a + b)^23.

Front

What is the relationship between the rows of Pascal's Triangle and the degrees of binomial expansions?

Back

Each row in Pascal's Triangle corresponds to the coefficients of the binomial expansion of (a + b)^n, where n is the row number.

Front

What is the sum of the elements in the nth row of Pascal's Triangle?

Back

The sum of the elements in the nth row of Pascal's Triangle is equal to 2^n.