Question

Find the tenth term of the expansion (x+ y)¹³

Select one
a 715x⁴y^9
b.75x^3y^9
615x⁴y^8
d. 13x^10 y^10​

Answer 1

`715x^4y^9`

Explanation:

Given

`(x + y)^{13`

Required

Determine the 10th term

Using binomial expansion, we have:

`(a + b)^n = ^nC_0a^nb^0 + ^nC_1a^(n-1)b^1 + ^nC_2a^(n-2)b^2 +.....+^nC_na^(0)b^n`

For, the 10th term. n = 9

So, we have:

`(a + b)^n = ^nC_(9)a^(n-9)b^{9`

`(x + y)^(13) = ^(13)C_(9)x^(13-9)y^9`

`(x + y)^(13) = ^(13)C_(9)x^4y^9`

Apply combination formula

`(x + y)^(13) = (13!)/((13-9)!9!)x^4y^9`

`(x + y)^(13) = (13!)/(4!9!)x^4y^9`

`(x + y)^(13) = (13*12*11*10*9!)/(4!9!)x^4y^9`

`(x + y)^(13) = (13*12*11*10)/(4!)x^4y^9`

`(x + y)^(13) = (13*12*11*10)/(4*3*2*1)x^4y^9`

`(x + y)^(13) = (17160)/(24)x^4y^9`

`(x + y)^(13) = 715x^4y^9`

Hence, the 10th term is
`715x^4y^9`