Question

Question 1. (3) Find the coefficient of $x^4y^2$ in the expansion of $(2x - y)^6$ without expanding.

Name: question 1 3 find the coefficient of x4y2 in the expansion of 2x y6 without expanding 15967
Uploaded: 2023-08-18T00:20:54-08:00
Duration: 4 min 3 s
Channel: Madhur L
Description: question 1 3 find the coefficient of x4y2 in the expansion of 2x y6 without expanding 15967

          Question 1. (3)
Find the coefficient of $x^4y^2$ in the expansion of $(2x - y)^6$ without expanding.

Added by Brad D.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Madhur L

08/18/2023

Step 1

Using the binomial theorem, the general term in the expansion of $(a+b)^n$ is given by $$T_{k+1} = \binom{n}{k} a^{n-k} b^k$$ In our case, $a = 2x$, $b = -y$, and $n = 6$. We want to find the term with $x^4y^2$. So we need $(2x)^{n-k} (-y)^k$ to have $x^4y^2$. Show more…

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