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Blizzard [7]
3 years ago
12

For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7

Mathematics
1 answer:
Sloan [31]3 years ago
5 0

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean 210x^6y^4

We can deduce that this term will be located somewhere in the middle. So I will calculate k= 5; k=6 \text{ and } k =7.

For k=5

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just x^{n-k} y^k

For k=6

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

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Answer: C

Step-by-step explanation:

We are given the information that:

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There are multiple ways to write this equation bu shifting around negative and positive values. Another way to write this equation would be (-2,500(x) + 50,000). That would be choice C.

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3 years ago
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Gnoma [55]

Step-by-step explanation:

Hey, there!!

a. (-12)×(-11)×10

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(-)×(-)=(+)

(-25)×(-8)=200

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= -400.

Therefore, the answer of a. no. is 1320, and no. b is (-400).

<em><u>Hope it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

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nata0808 [166]
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Ede4ka [16]

Answer:

108

Step-by-step explanation:

It is a geometric sequence, so you're always multiplying or dividing by the same amount.

Here, you're multiplying each term by 3 to get the next one.

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You can then check if this answer is correct by dividing the next term (324) by 3 to see if you get 108.

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3 years ago
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