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Demonstrate how to multiply two binomials - Computers & Internet

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  1. Adding and Subtracting Binomials
    • 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.

    • 9

      Divide each term in the binomial by the divisor; (18x^3 / 3x) + (9x^2 / 3x) = 6x^2 + 3x.

Posted on May 10, 2014

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I need to understand how to divide a binomial.


Let's take 2x^2 - 10x +12 and divide it by x-2.
__2x_-_6____________
x-2 ) 2x^2 - 10x + 12
2x^2 - 4x
------------
- 6x + 12
- 6x + 12
------------
0


How many times does x go into 2x^2. Put the answer, 2x above the 2x^2. Next mulitply (x-2) by 2x and put the answer under 2x^2. Now subtract that answer from 2x^2 - 10x and we get -6x (-10x - (-4x)).

How many time does x go into -6x. -6 time. Write this above the line and put the answer above the -10x. Next multiply (x-2) by -6 and put the answer under the -6x. Subtract and we get 0 and we are done. If we want to check our answer we can multiply (x-2) and (2x - 6) and we should get 2x^2 - 10 x + 12.

Good luck.

Paul

Oct 03, 2014 | Office Equipment & Supplies

1 Answer

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)

Jun 02, 2014 | Computers & Internet

1 Answer

Texas 30XIIB binomial cdf


The only known equation for the cumulative binomial distribution is the sum of the individual binomial probabilities. Some more sophisticated (and more expensive) calculators have that equation built in, but the 30xii does not.

If n>30 and n*p>5 and n*(1-p)>5 then you can approximate the cumulative binomial with the normal probability function, but again the 30xii does not have that built in.

Apr 14, 2014 | Texas Instruments TI-30 XIIS Calculator

1 Answer

Binompdf binomial binomcdf


Do you have a question about the binomial probability distribution function or the binomial cumulative distribution function?

Nov 14, 2013 | Casio FX570ES Scientific Calculator

1 Answer

(3n+2)(n+3)


To multiply binomials use the mnemonic FOIL
  1. Multiply the FIRST members of the two binomials: 3n*n=3n^2
  2. Multiply the OUTER members of expression when read from left (3n) to right (3) =9n
  3. Multiply the INNER members 2 *n=2n
  4. Multiply the LAST members of the binomials 2*3=6
  5. Add all the products 3n^2+ 9n+2n+6,
then combine the two like-terms 9n+2n=11n
Result is 3n^2+11n+6
Seriously now: what does this have to do with Printers and Copiers?

Sep 21, 2013 | Office Equipment & Supplies

1 Answer

Cube binomials


What would you like to know about that cube binomial?

Aug 21, 2013 | Computers & Internet

1 Answer

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:

x-y-2-diagram.gif
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
so:

(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

Jul 26, 2011 | Computers & Internet

2 Answers

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.
2.gif
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.
6.gif

Jun 12, 2011 | Computers & Internet

1 Answer

I was told that, to do binomial distributions on a ti-86, I would need to hit 2nd Math, then More, and I should see something that says STAT and go from there to get to DIST and Binomi. I see nothing...


Hello,

Sorry, but you information is wrong, to find the binomial distribution use the PROB menu not the STAT menu. Its name is randBi
[2nd][MATH][F2:PROB] scroll right.
Hope it helps.

Oct 10, 2009 | Texas Instruments TI-86 Calculator

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