Exercises: Apply the Binomial Theorem

This is an advanced (+) topic. Work through each section in order, showing all steps for expansion problems.

Grade 11·21 problems·~42 min·Common Core Math - HS Algebra·standard·hsa-apr-c-5

Work through problems with immediate feedback

Recall / Warm-Up

In Row 4 of Pascal's Triangle, what are the five entries (left to right)?

1, 3, 3, 1

1, 4, 6, 4, 1

1, 4, 4, 4, 1

1, 5, 10, 10, 5, 1

Which value of $0!$ is used in the Binomial Theorem?

$0! = 0$

$0! = 1$

$0!$ is undefined

$0! = 0!$ (it cancels itself)

In the expansion of $(x + y)^n$ , how many terms are there?

$n$ terms

$n + 1$ terms

$2n$ terms

$n^2$ terms

$Pascal's Triangle rows 0 through 5, with Row 5 highlighted and the entry C(5,2)=10 circled to show the coefficient of x^3y^2 in (x+y)^5.$

Which entry in Pascal's Triangle corresponds to the coefficient of $x^3y^2$ in the expansion of $(x + y)^5$ ?

Row 5, position 2 (from left, starting at position 0): $C(5, 2) = 10$

Row 5, position 3: $C(5, 3) = 10$

Row 5, position 3: $C(5, 3) = 10$ — these are the same, since $C(5,2) = C(5,3) = 10$

Row 3, position 2: $C(3, 2) = 3$

Compute the binomial coefficient $C(6, 2)$ using the formula $C(n, k) = \frac{n!}{k!(n-k)!}$ .

Enter the value of $C(6, 2)$ .

Use Pascal's Triangle (Row 4) to expand $(x + y)^4$ . What is the coefficient of the $x^2y^2$ term?

What is the coefficient of the $x^2y^2$ term in the expansion of $(x - y)^4$ ?

$6$

$-6$

$4$

$-4$

What is the 3rd term of $(x + y)^7$ ? (Term counting starts at 1.)

$C(7, 3) \cdot x^4 y^3 = 35x^4y^3$

$C(7, 2) \cdot x^5 y^2 = 21x^5y^2$

$C(7, 3) \cdot x^3 y^4 = 35x^3y^4$

$C(7, 1) \cdot x^6 y^1 = 7x^6y$

Find the coefficient of the $x^3y^5$ term in the expansion of $(x + y)^8$ .

Enter the coefficient.

You're viewing 2 of 6 sections.

Create a free account to continue the full exercise set and save your progress.

0 of 9 answered

Answer all problems to submit.