Pascal's Triangle Review

Front

What is Pascal's Triangle?

Back

A triangular array of the binomial coefficients, where each number is the sum of the two directly above it.

Front

How do you find the coefficients for the expansion of (a + b)^n using Pascal's Triangle?

Back

The coefficients are found in the nth row of Pascal's Triangle.

Front

What is the relationship between the row number and the exponent in a binomial expansion?

Back

The row number corresponds to the exponent of the binomial.

Front

What is the formula for the binomial expansion of (x + y)^n?

Back

The expansion is given by the sum of C(n, k) * x^(n-k) * y^k for k = 0 to n, where C(n, k) is the binomial coefficient.

Front

What is the binomial coefficient C(n, k)?

Back

C(n, k) = n! / (k!(n-k)!), representing the number of ways to choose k elements from a set of n elements.

Front

What is the value of C(4, 2)?

Back

C(4, 2) = 4! / (2! * 2!) = 6.

Front

What is the expansion of (x + 3)^3?

Back

x^3 + 9x^2 + 27x + 27.

Front

What is the expansion of (x - 2)^5?

Back

x^5 - 10x^4 + 40x^3 - 80x^2 + 64.

Front

What is the expansion of (x + y)^5?

Back

x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5.

Front

How do you determine the number of terms in the expansion of (a + b)^n?

Back

The number of terms is n + 1.