Answer:
[tex]715x^4y^9[/tex]
Step-by-step explanation:
Given
[tex](x + y)^{13[/tex]
Required
Determine the 10th term
Using binomial expansion, we have:
[tex](a + b)^n = ^nC_0a^nb^0 + ^nC_1a^{n-1}b^1 + ^nC_2a^{n-2}b^2 +.....+^nC_na^{0}b^n[/tex]
For, the 10th term. n = 9
So, we have:
[tex](a + b)^n = ^nC_{9}a^{n-9}b^{9[/tex]
[tex](x + y)^{13} = ^{13}C_{9}x^{13-9}y^9[/tex]
[tex](x + y)^{13} = ^{13}C_{9}x^4y^9[/tex]
Apply combination formula
[tex](x + y)^{13} = \frac{13!}{(13-9)!9!}x^4y^9[/tex]
[tex](x + y)^{13} = \frac{13!}{4!9!}x^4y^9[/tex]
[tex](x + y)^{13} = \frac{13*12*11*10*9!}{4!9!}x^4y^9[/tex]
[tex](x + y)^{13} = \frac{13*12*11*10}{4!}x^4y^9[/tex]
[tex](x + y)^{13} = \frac{13*12*11*10}{4*3*2*1}x^4y^9[/tex]
[tex](x + y)^{13} = \frac{17160}{24}x^4y^9[/tex]
[tex](x + y)^{13} = 715x^4y^9[/tex]
Hence, the 10th term is [tex]715x^4y^9[/tex]
