Respuesta :
(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
Answer:
6854640
Step-by-step explanation:
Binomial expansion:
[tex]\left(a+b\right)^n=\sum _{r=0}^n\binom{n}{r}a^{\left(n-r\right)}b^r[/tex]
Term where power of second term is r.
[tex]Term=\binom{n}{r}a^{\left(n-r\right)}b^r[/tex]
The given expression is
[tex](13a^2-4b)^6[/tex]
here, n=6.
We need to find the coefficient of the term [tex]a^8b^2[/tex].
Power of b is 2, so the value of r is 2.
Using binomial expansion, we can find the term [tex]a^8b^2[/tex] with its coefficient.
[tex]=\binom{6}{2}(13a^2)^{\left(6-2\right)}(-4b)^2[/tex]
[tex]=\frac{6!}{2!\left(6-2\right)!}\left(13a^2\right)^4\left(-4b\right)^2[/tex]
[tex]=15(13)^4(a^2)^4(-4)^2(b)^2[/tex]
[tex]=6854640a^8b^2[/tex]
Therefore, the coefficient of the term [tex]a^8b^2[/tex] is 6854640.
