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fgiga [73]
2 years ago
9

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

Mathematics
1 answer:
Anon25 [30]2 years ago
3 0

Answer:

715x^4y^9

Step-by-step 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} = \frac{13!}{(13-9)!9!}x^4y^9

(x + y)^{13} = \frac{13!}{4!9!}x^4y^9

(x + y)^{13} = \frac{13*12*11*10*9!}{4!9!}x^4y^9

(x + y)^{13} = \frac{13*12*11*10}{4!}x^4y^9

(x + y)^{13} = \frac{13*12*11*10}{4*3*2*1}x^4y^9

(x + y)^{13} = \frac{17160}{24}x^4y^9

(x + y)^{13} = 715x^4y^9

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

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