41.0k views
2 votes
What is the numerical coefficient of the a8b2 term in the expansion of (13a2−4b)6

2 Answers

3 votes

(13a^2 - 4b)^6 = (13a^2)^6 + 6C1 (13a^2)^5 (-4b)^1 + 6C2 (13a^2)^4 * (-4b)2

The last of the above terms has a^8b^2 as part of it so the required numerical coefficient = 6C2 * 13^4 * (-4)^2

= 15*28561* 16

= 6,854,640 Answer

User Mateus Pinheiro
by
8.0k points
1 vote

Answer:

6854640

Explanation:

Binomial expansion:


\left(a+b\right)^n=\sum _(r=0)^n\binom{n}{r}a^(\left(n-r\right))b^r

Term where power of second term is r.


Term=\binom{n}{r}a^(\left(n-r\right))b^r

The given expression is


(13a^2-4b)^6

here, n=6.

We need to find the coefficient of the term
a^8b^2.

Power of b is 2, so the value of r is 2.

Using binomial expansion, we can find the term
a^8b^2 with its coefficient.


=\binom{6}{2}(13a^2)^(\left(6-2\right))(-4b)^2


=(6!)/(2!\left(6-2\right)!)\left(13a^2\right)^4\left(-4b\right)^2


=15(13)^4(a^2)^4(-4)^2(b)^2


=6854640a^8b^2

Therefore, the coefficient of the term
a^8b^2 is 6854640.

User Nihulus
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories