Binomial Theorem

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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 does (2x + 5)^4 expand to using the Binomial Theorem?

Back

(2x + 5)^4 = 16x^4 + 160x^3 + 600x^2 + 1000x + 625.

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.

Tags

CCSS.HSA.APR.C.5

Front

What is row 7 of Pascal's Triangle?

Back

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

Tags

CCSS.HSA.APR.C.5

Front

What is the formula for the binomial coefficient (n choose k)?

Back

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

Tags

CCSS.HSA.APR.C.5

Front

How do you calculate (a + b)^3 using the Binomial Theorem?

Back

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.

Tags

CCSS.HSA.APR.C.5

Front

What is the significance of the coefficients in the expansion of (a + b)^n?

Back

The coefficients correspond to the values in row n of Pascal's Triangle.

Tags

CCSS.HSA.APR.C.5

Front

What is the general term in the expansion of (a + b)^n?

Back

The general term is T(k+1) = (n choose k) * a^(n-k) * b^k.

Tags

CCSS.HSA.APR.C.5

Front

Expand (x + 2)^5 using the Binomial Theorem.

Back

(x + 2)^5 = x^5 + 10x^4 * 2 + 40x^3 * 4 + 80x^2 * 8 + 32.

Tags

CCSS.HSA.APR.C.5

Front

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

Back

(3 + 4)^2 = 3^2 + 2*3*4 + 4^2 = 9 + 24 + 16 = 49.

Tags

CCSS.HSA.APR.C.5