Question about Bagatrix Algebra Solved! 2005 (105101) for PC

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1.01^1000000 is greater or 10000 ?

This has to be solved using binomial theorem

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Re: 1.01^1000000 is greater or 10000 ?

Try this... here we represent 1.01 as 1+.01
and so we have nCr and stuff... it can be noted that a number lesser than .01 when raised to power will result in a number lesser than it and hence the first term which is 1^1000000 will be greatest among the terms... so it can never be greater than 10000

Posted on Jan 31, 2008

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Re: 1.01^1000000 is greater or 10000 ?

I am sorry to come in like that (5 years after the question was asked) and spoil your fun.
If you try to enter it on a regular calculator you will get an overflow error, memory error or some such thing. On the Windows calculator here is what I get.

Posted on Mar 01, 2013

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Examples of square of a binomial

A binomial has two terms, like (a+b).
The square of a binomial has three terms:
(a+b)**2 = a**2 + 2ab + B**2 (where **2 means squared)

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Demonstrate how to multiply two binomials

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    • 1

      Arrange each term in each binomial in order of degree from greatest to least. The degree of a binomial is the exponent attached to the term. For example, 4x^2 is a second degree term.

    • 2

      Multiply each term in the binomial that is being subtracted by -1 to turn it into an addition problem. For example, the problem (8x^2 + 8) - (x^2 - 2) becomes (8x^2 + 8) + (-x^2 + 2).

    • 3

      Combine like terms. In the example problem, the x^2 terms are combined and the constant terms are combined, yielding (8x^2 + 8) + (-x^2 + 2) = 7x^2 + 10.

    Multiplying Binomials
    • 4

      Understand the F.O.I.L. method. F.O.I.L. is an acronym standing for first, outside, inside and last. It means that you multiply the first number of the first binomial by the first number of the second, then the numbers on the outside (the first term of the first binomial by the second term of the second binomial) and so on. This ensures that both numbers in the first binomial are multiplied by both numbers in the second.

    • 5

      Use the F.O.I.L. method to multiply the two binomials together. For example, (3x + 4)(3x - 4) = 9x^2 +12x - 12x - 16. Notice that -12x is the product of the outside terms and -16 is the product of the last terms, 4 and -4.

    • 6

      Simplify. There will almost always be like terms to combine. In the example, 12x and -12x cancel out, yielding the answer 9x^2 - 16.

    Dividing Binomials
    • 7

      Use the distributive property to divide both terms in the binomial by the monomial divisor. For example, (18x^3 + 9x^2) / 3x = (18x^3 / 3x) + (9x^2 / 3x).

    • 8

      Understand how to divide by a term. If you are dividing a higher order term by a lower order term, you subtract the exponent. For example, y^3/y = y^2. The number part of each term is handled like any other division problem. For example, 20z / 4 = 5z.

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Definition of special product types and examples of special products

In mathematics, special products are of the form:
(a+b)(a-b) = a2 - b2 (Product of sum and difference of two terms) which can be used to quickly solve multiplication such as:
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1. Square of a binomial
(a+b)^2 = a^2 + 2ab + b^2
carry the signs as you solve

2. Square of a Trinomial
(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc
carry the sings as you solve

3. Cube of a Binomial
(a+b)^3 = a^3 + 3(a^2)b + 3a(b^2) + b^3

4. Product of sum and difference
(a+b)(a-b) = a^2 - b^2

5. Product of a binomial and a special multinomial
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Jul 28, 2011 | Educational & Reference Software

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Definition of special product in algebra types and example of special product in algebra

Product means the result you get after multiplying.
In Algebra xy means x multiplied by y
Likewise when you see (a+b)(a-b) it means (a+b) multiplied by (a-b), which we will be using a lot here!
Special Binomial Products So when you multiply binomials you get ... Binomial Products
And we are going to look at three special cases of multiplying binomials ... so they are Special Binomial Products.
1. Multiplying a Binomial by Itself What happens when you square a binomial (in other words, multiply it by itself) .. ?

(a+b)2 = (a+b)(a+b) = ... ?

The result:

(a+b)2 = a2 + 2ab + b2
You can easily see why it works, in this diagram:

2. Subtract Times Subtract And what happens if you square a binomial with a minus inside?

(a-b)2 = (a-b)(a-b) = ... ?

The result:

(a-b)2 = a2 - 2ab + b2
3. Add Times Subtract And then there is one more special case... what if you multiply (a+b) by (a-b) ?

(a+b)(a-b) = ... ?

The result:

(a+b)(a-b) = a2 - b2
That was interesting! It ended up very simple.
And it is called the "difference of two squares" (the two squares are a2 and b2).
This illustration may help you see why it works:
apb-amb-why.gif a2 - b2 is equal to (a+b)(a-b) Note: it does not matter if (a-b) comes first:

(a-b)(a+b) = a2 - b2
The Three Cases Here are the three results we just got:
(a+b)2 = a2 + 2ab + b2 } (the "perfect square trinomials") (a-b)2 = a2 - 2ab + b2 (a+b)(a-b) = a2 - b2 (the "difference of squares") Remember those patterns, they will save you time and help you solve many algebra puzzles.
Using Them So far we have just used "a" and "b", but they could be anything.
Example: (y+1)2
We can use the (a+b)2 case where "a" is y, and "b" is 1:

(y+1)2 = (y)2 + 2(y)(1) + (1)2 = y2 + 2y + 1

Example: (3x-4)2
We can use the (a-b)2 case where "a" is 3x, and "b" is 4:

(3x-4)2 = (3x)2 - 2(3x)(4) + (4)2 = 9x2 - 24x + 16

Example: (4y+2)(4y-2)
We know that the result will be the difference of two squares, because:

(a+b)(a-b) = a2 - b2

(4y+2)(4y-2) = (4y)2 - (2)2 = 16y2 - 4
Sometimes you can recognize the pattern of the answer:
Example: can you work out which binomials to multiply to get 4x2 - 9
Hmmm... is that the difference of two squares?
Yes! 4x2 is (2x)2, and 9 is (3)2, so we have:

4x2 - 9 = (2x)2 - (3)2
And that can be produced by the difference of squares formula:

(a+b)(a-b) = a2 - b2
Like this ("a" is 2x, and "b" is 3):

(2x+3)(2x-3) = (2x)2 - (3)2 = 4x2 - 9
So the answer is that you can multiply (2x+3) and (2x-3) to get 4x2 - 9

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How to solve foil method

The FOIL Method is a process used in algebra to multiply two binomials. The lesson on the Distributive Property, explained how to multiply a monomial or a single term such as 7 by a binomial such as (4 + 9x).
1.gif But, what if there was a binomial instead of a single term outside of the parentheses? That is, what if a binomial was being multiplied by another binomial? An example of this is given below.
FOIL stands for:
First - Multiply the first term in each set of parentheses Outer - Multiply the outer term in each set of parentheses Inner - Multiply the inner term in each set of parentheses Last - Multiply the last term in each set of parentheses Now let's give it a try in our problem. We'll start by multiplying the first term in each set of parentheses and then marking down the answer below the problem.
3.gif Now we will multiply the outer terms and again mark down the answer below the problem.
4.gif And the Inners.
5.gif And finally the last terms.

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What type of problem is this (9x-7)-4(3x 5)

just a simple multiplication solve first which is inside the brackets 9x(-7)=-63 3x5=15 (-63)-4x15 -67x15 -1005 .. i think am rite..

Oct 12, 2008 | SoftMath Algebrator - Algebra Homework...

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