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3 years ago

Apply the Binomial Theorem to the expression (x^2+1)^2

Mathematics

2 answers:

timurjin [86]3 years ago

8 0

Answer:

x^4 + 2x^2 + 1

Step-by-step explanation:

Using Pascal's Triangle, we end up with the following set of coefficients in a triangular form:

1 2 1

The coefficients 1, 2 and 1 are used as follows:

1(x^2)^2 + 2(x^2) + 1(1)^2, or

x^4 + 2x^2 + 1

Therefore the given expression (x^2+1)^2 is equivalent to the expanded form x^4 + 2x^2 + 1 .

KiRa [710]3 years ago

6 0

Answer:

Step-by-step explanation:

(x^2 +1)(x^2 +1)

x^4 +x^2+x^2 +1

x^4+2x^2 +1 answer

Hope this helps!

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How do I Simplify 4a – 7b + 2ab – a + b (I need step by step cause I'm trying to learn this)

Alex

Step-by-step explanation:

Ok. First of all, we need to follow the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. We don't have any parentheses, exponents, or division to resolve, so you can skip those. So now you have: Multiplication, Addition, and Subtraction. We have multiplication in each term, but each term is fully simplified, so we have Addition and Subtraction left.

With that out of the way, let's go ahead and rearrange this equation so it is easier to solve. (<em>Note: we can only rearrange terms that are positive because subtraction is not commutative. But we can turn negative terms into "positive" terms by the method shown below.</em>)

4a - 7b + 2ab - a + b

4a + (-7b) + 2ab + (-a) + b (<em>Now the terms are all positive, so we can rearrange them, but they still have the same value.</em>)

4a + (-a) + 2ab + (-7b) + b

3a + 2ab + 7b

And there we go. Our answer is fully simplified. If you can understand this, you'll be able to simplify without isolating and rearranging the terms each time.

Hopefully this was helpful and not confusing.

4 0

2 years ago

What is the mean of this table

suter [353]

Answer:

The mean is 77.8125

Step-by-step explanation:

The mean is the average of the numbers. It is very easy to calculate and get. All you have to do is add up all the numbers and divide it by how many numbers there are.

80 + 90 + 81 + 86 + 100 + 77 + 75 + 96 + 65 + 87 + 58 + 80 + 36 + 73 + 70 + 91 = 1245

$\frac{1245}{16} = 77.8125$

7 0

2 years ago

HELPPPPPPPPPPPPPPPPP

igomit [66]

X=3
LOM and KOL are equivalent, so the equation is 43=6x+25 :)

5 0

2 years ago

Find the 95% confidence interval for estimating the population mean μ

AVprozaik [17]

We first need to determine whether we are dealing with means or proportions in this problem. Since we are given the sample and population mean, we know that we are dealing with means.

Since we have one sample mean, this means we are creating a confidence interval for one sample (1 Samp T Int).

Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.

<h3>Confidence Interval Formula</h3>

The formula for constructing a <u>confidence interval for means</u> is as follows: