Coefficient of X¹⁸ in the expansion of (ax⁴-bx)⁹

Subject:
Math
Author:
jaylahb3sp
Created:
1 year ago

Answers 2

Answer:

Let's write it as x

(ax

−b), general term in its expansion will be

(ax

)

(−b)

n−r

where r varies from 0 to n.

Power of x is 18 ⇒ 9+3r=18

⇒r=3

Coefficient of x

=84a

Step-by-step explanation:

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Author:

pigletkyqu
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Answer:

[tex]= > \ ^9C_6\ a^3\ b^6[/tex]

Step-by-step explanation:

[tex]= > T_{r+1}=\ ^n{C_r}\ x^{n-r} \ y^r[/tex]

[tex]= > T_{r+1}=\ ^9C_r\ (ax^4)^{9-r}\ (-bx)^r[/tex]

[tex]= > T_{r+1}=\ ^9C_{r}\ a^{9-r}\ (-b)^r\ x^{36-4r}.x^r[/tex]

[tex]= > T_{r+1}=\ ^9C_{r}a^{9-r}(-b)^r.x^{36-3r}[/tex]

[tex]We\:\ need\:\ coefficient\:\ of\:\ x^{18}[/tex]

=> 36 - 3r = 18

=>3r = 18

=> r = 6

Therefore Coefficient is

[tex]= > \ ^9C_6\ a^3\ b^6[/tex]

Author:

petersen
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