Binomial Theorem

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What is the Binomial Theorem?

Back

The Binomial Theorem provides a formula for the expansion of powers of binomials. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n.

Tags

CCSS.HSA.APR.C.5

Front

What are the coefficients in the expansion of (x + y)^n?

Back

The coefficients are given by the binomial coefficients, which can be found in Pascal's Triangle or calculated using the formula n choose k.

Tags

CCSS.HSA.APR.C.5

Front

How do you find the coefficients of the 5th row in Pascal's Triangle?

Back

The coefficients of the 5th row are found by calculating the binomial coefficients for n=5: 1, 5, 10, 10, 5, 1.

Tags

CCSS.HSA.APR.C.5

Front

Expand (x - 7)^2 using the Binomial Theorem.

Back

The expansion is x^2 - 14x + 49.

Tags

CCSS.HSA.APR.C.5

Front

What is the 2nd term in the expansion of (y + 4)^4?

Back

The 2nd term is 16y^3.

Tags

CCSS.HSA.APR.C.5

Front

What is row 7 of Pascal's Triangle?

Back

Row 7 is 1, 7, 21, 35, 35, 21, 7, 1.

Tags

CCSS.HSA.APR.C.5

Front

What is the Binomial expansion of (x + 1)^5?

Back

The expansion is x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1.

Tags

CCSS.HSA.APR.C.5

Front

What is the formula for the binomial coefficient?

Back

The binomial coefficient is given by n choose k = n! / (k!(n-k)!).

Tags

CCSS.HSA.APR.C.5

Front

What does the term 'n choose k' represent?

Back

'n choose k' represents the number of ways to choose k elements from a set of n elements without regard to the order of selection.

Front

How can you use Pascal's Triangle to find binomial coefficients?

Back

Each row of Pascal's Triangle corresponds to the coefficients of the binomial expansion for increasing powers of (a + b).

Tags

CCSS.HSA.APR.C.5