So the sum of 17 and a number x means to add them on one side of the equals sign. The other side would be your 20.
17 + x = 20
<span>binomial </span>is an algebraic expression containing 2 terms. For example, (x + y) is a binomial.
We sometimes need to expand binomials as follows:
(a + b)0 = 1
(a + b)1 = a + b
(a + b)2 = a2 + 2ab + b2
(a + b)3 = a3 + 3a2b + 3ab2 + b3
<span>(a + b)4</span> <span>= a4 + 4a3b</span><span> + 6a2b2 + 4ab3 + b4</span>
<span>(a + b)5</span> <span>= a5 + 5a4b</span> <span>+ 10a3b2</span><span> + 10a2b3 + 5ab4 + b5</span>
Clearly, doing this by direct multiplication gets quite tedious and can be rather difficult for larger powers or more complicated expressions.
Pascal's Triangle
We note that the coefficients (the numbers in front of each term) follow a pattern. [This was noticed long before Pascal, by the Chinese.]
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
You can use this pattern to form the coefficients, rather than multiply everything out as we did above.
The Binomial Theorem
We use the binomial theorem to help us expand binomials to any given power without direct multiplication. As we have seen, multiplication can be time-consuming or even not possible in some cases.
<span>Properties of the Binomial Expansion <span>(a + b)n</span></span><span><span>There are <span>\displaystyle{n}+{1}<span>n+1</span></span> terms.</span><span>The first term is <span>an</span> and the final term is <span>bn</span>.</span></span><span>Progressing from the first term to the last, the exponent of a decreases by <span>\displaystyle{1}1</span> from term to term while the exponent of b increases by <span>\displaystyle{1}1</span>. In addition, the sum of the exponents of a and b in each term is n.</span><span>If the coefficient of each term is multiplied by the exponent of a in that term, and the product is divided by the number of that term, we obtain the coefficient of the next term.</span>
I'm sorry no one can answer and where is the question?
Please put in the question and I might be able to help!
Answer:
The three digit number = 951
Step-by-step explanation:
Let suppose the numbers are:
= abc
According to given condition:
a+ b + c = 15 -------------eq1
Also, given the difference between the first two digit = the difference between the last two digits:
==> l a-b l = l b-cl
==> (a-b) = (b-c)
==> (a+c) = 2b
Now we will substitue in eq1
==> a+ b + c = 15
==> 2b + b = 15
==> 3b = 15
Dividing both sides by 3 we get:
b =5
a + c = 2b
a+ c = 10
a = 10 -c ..........(2)
We know that"
(a-b) = (b-c)
==> a > b+c
==> a > 5 + c
==> 10 -c > 5 +c
==>5 > 2c
==> 2.5 > c
As c is an odd number so c will be equal to 1
c = 1
a = 10 -1
a = 9
The three digit number = 951
The hundred digit is greater than the sum of the tens and ones digits
i hope it will help you!
Answer:
32 +6y^2+
Step-by-step explanation:
