Back to Tutor Intake Assessment: Apply the Binomial Theorem

HSA.APR.C.5 Tutor Intake — Binomial Theorem and Pascal's Triangle

This short check helps your tutor understand where to start with the Binomial Theorem. Answer each question on your own without help. If you are unsure, give your best try. (Note: This is an advanced topic marked (+).)

Grade 11·5 problems·~10 min·Common Core Math - HS Algebra·standard·hsa-apr-c-5

Work through problems with immediate feedback

Concepts

Which row of Pascal's Triangle gives the coefficients for the
expansion of $(x + y)^4$ ?

$1 \quad 3 \quad 3 \quad 1$

$1 \quad 4 \quad 6 \quad 4 \quad 1$

$1 \quad 5 \quad 10 \quad 10 \quad 5 \quad 1$

$1 \quad 4 \quad 4 \quad 1$

Compute $\binom{6}{2} = \dfrac{6!}{2!\,4!}$ .

Enter the value.

Procedures

Use Pascal's Triangle to expand $(x + y)^4$ .
The coefficients are $1, 4, 6, 4, 1$ .

In the expansion, what is the coefficient of $x^2 y^2$ ?

Find the 3rd term of $(x + y)^8$ .

The $k$ th term (counting from 1) is $\binom{8}{k-1} x^{8-(k-1)} y^{k-1}$ .

Enter the coefficient of the 3rd term.

You're viewing 2 of 3 sections.

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

Create free account

0 of 4 answered

Answer all problems to submit.