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Which is the value of the 3rd term in the expansion of (x+6)*6?

User Farzam
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1 Answer

1 vote

Answer:

540x⁴

Explanation:

You want the 3rd term of the expansion of (x +6)⁶.

Binomial expansion

The k-th term of (a +b)^n is ...

C(n, k)a^(n-k)b^k

where terms are numbered 0 to n.

Third term

The third term of (x+6)⁶ is the above expression with k=2:

C(6, 2)a⁴b²

Where a=x and b=6, this is ...

15x⁴6² = 540x⁴

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Additional comment

C(n, k) is the function that represents the number of combinations of n things taken k at a time:

C(n, k) = n!/(k!(n-k)!)

C(6, 2) = 6!/(2!·4!) = 6·5/(2·1) = 15

User Grayger
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