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Semenov [28]
3 years ago
7

How to find the fourth term of a binomial expansion?

Mathematics
1 answer:
Kipish [7]3 years ago
4 0
So let's look at how to expand a binomial..
Start with just the variable exponents which will be numbered in ascending and descending order.

example (without coefficients)
(x+y)^3 = x^3(y^0) + x^2(y^1) + x^1(y^2) + x^0(y^3)

If the binomial is (x-y)^3 the +/- signs will toggle like so.. (again leaving out coefficients)
(x-y)^3 = x^3(y^0) - x^2(y^1) + x^1(y^2) - x^0(y^3)

If there is a coefficient or power inside the binomial like (x^2+2y)^3 these are also raised to the appropriate power.

(x^2+2y)^3 = (x^2)^3(y^0)(2^0) + (x^2)^2(y^1)(2^1) + ....

now there are also coefficients for each term which follow a combination pattern of Pascal triangle. C(3,0) ; C(3,1) ; C(3,2) ; C(3,3)
these get multiplied by each term.

So the 4th term of (x^2-2y)^3
will be negative
have coefficient of: C(3,3) * (2^3) = 8
variables: x^0(y^3) = y^3
= -8y^3
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What decimal does this model represent? Explain.<br> Online Pearson Realize com
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Oliva ties 2.5 feet of ribbon on to 1 balloon how many yards of ribbon dose olivia need for 18 balloons
Bezzdna [24]

Olivia needs 15 yards of ribbon.

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4 0
3 years ago
A firm manufactured 1000 Tv sets during its first yeae the total firns production during 10 years of operation is 29035 sets If
Alexus [3.1K]

Answer: the increase each year is 423 tv sets

Step-by-step explanation:

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

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n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

n = 10 years

a = 1000

S10 = 29035

We want to determine d which is the amount by which the production increased each year. Therefore, the sum of the first 10 years would be

29035 = 10/2[2 × 1000 + (10 - 1)d]

29035 = 5[2000 + 9d]

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9d = 5807 - 2000 = 3807

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3 years ago
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