Binomial Theorem

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. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

Tags

CCSS.HSA.APR.C.5

Front

What is Pascal's Triangle?

Back

Pascal's Triangle is a triangular array of the binomial coefficients. Each number is the sum of the two directly above it, and it is used to find coefficients in the expansion of binomials.

Tags

CCSS.HSA.APR.C.5

Front

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

Back

The coefficients of the expansion of (a + b)^n correspond to the nth row of Pascal's Triangle.

Tags

CCSS.HSA.APR.C.5

Front

What is the formula for the binomial coefficient, often denoted as 'n choose k'?

Back

The binomial coefficient is given by the formula C(n, k) = n! / (k!(n-k)!), where n! is the factorial of n.

Tags

CCSS.HSA.APR.C.5

Front

What is row 0 of Pascal's Triangle?

Back

Row 0 of Pascal's Triangle is simply 1.

Tags

CCSS.HSA.APR.C.5

Front

What is the significance of row 1 in Pascal's Triangle?

Back

Row 1 of Pascal's Triangle is 1, 1, which corresponds to the coefficients of (a + b)^1.

Tags

CCSS.HSA.APR.C.5

Front

Expand the expression (x + 2)^3 using the Binomial Theorem.

Back

The expansion is x^3 + 6x^2 + 12x + 8.

Tags

CCSS.HSA.APR.C.5

Front

What is the value of (3 + 4)^2 using the Binomial Theorem?

Back

Using the Binomial Theorem, (3 + 4)^2 = 3^2 + 2(3)(4) + 4^2 = 9 + 24 + 16 = 49.

Tags

CCSS.HSA.APR.C.5

Front

What is the relationship between the rows of Pascal's Triangle and the powers of binomials?

Back

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

Tags

CCSS.HSA.APR.C.5

Front

How do you calculate the 5th row of Pascal's Triangle?

Back

The 5th row of Pascal's Triangle is calculated as 1, 5, 10, 10, 5, 1, which corresponds to the coefficients of (a + b)^5.

Tags

CCSS.HSA.APR.C.5