Can u help me with definition of special products?

Polynomials that have to be squared, cubed etc. and solved mentally

Posted on Feb 09, 2011

Special product is RTOOOOT!! :)

Posted on Aug 05, 2012

SOURCE: definition of special product in

**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:

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**

Posted on Aug 09, 2011

SOURCE: definition of special product types and

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:

301 * 299 = (300 +1)(300-1) = 3002 - 12 = 90000 - 1 = 89999** types**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

(a+b)(a^2 - ab + b^2) = a^3-b^3

(a-b)(a^2 + ab + b^2) = a^3-b^3

Posted on Aug 18, 2011

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Posted on Jan 02, 2017

Definition of Diagnostic Trouble Code P0171
Category:
Powertrain
Definition:
System Too Lean Bank 1**Note**: This definition of P0171 is applied to all manufacturers

passenger o2 sensor,replace it

passenger o2 sensor,replace it

Jul 05, 2015 | Cars & Trucks

No need to coin a new word: Polynomial is the accepted form. Review the definition of binomial and polynomial, Choose one indeterminate (variable) X or Y, and create the entities (aX+b)* (cX^5+dX^3+ ....+ 25)

Jun 06, 2014 | Activision Computers & Internet

In algebra there are some identities (that are true all the time)

**(a+b)^2 is always equal to a^2+2ab+b^2**, regardless of the values of a and b. Another one **(a-b)^2=a^2-2ab+b^2**, and

**a^2-b^2=(a-b)(a+b)**

There is also the binomial identity**(a+b)^n.** Look this one up.

There is also the binomial identity

Jun 05, 2014 | Computers & Internet

I worked out the algebra leaving out a few simple steps (special binomial products, Pythagorean theorem in trigonometry, definition of secant and co-secant functions). I am inserting the answer as a set of png pictures. However I am not sure how it will look.

Sep 21, 2013 | ValuSoft Bible Collection (10281) for PC

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:

301 * 299 = (300 +1)(300-1) = 3002 - 12 = 90000 - 1 = 89999__types__

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

(a+b)(a^2 - ab + b^2) = a^3-b^3

(a-b)(a^2 + ab + b^2) = a^3-b^3

(a+b)(a-b) = a2 - b2 (Product of sum and difference of two terms) which can be used to quickly solve multiplication such as:

301 * 299 = (300 +1)(300-1) = 3002 - 12 = 90000 - 1 = 89999

(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

(a+b)(a^2 - ab + b^2) = a^3-b^3

(a-b)(a^2 + ab + b^2) = a^3-b^3

Jul 28, 2011 | Computers & Internet

In Algebra

Likewise when you see

Special Binomial Products So when you multiply binomials you get ... Binomial Products

And we are going to look at

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:

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

hemmings motor news

google it as it has been a loooong time since I had to do "old school' car work and research

google it as it has been a loooong time since I had to do "old school' car work and research

Aug 13, 2009 | 1983 Dodge Charger

I am also experiencing this problem, as well as 2 other people that I found on google, so I am inclined to think tha 3M has changed something in their manufacturing process, I think it very odd that this problem is manifesting itself at this time in different locations.

I have been using this product for sometime, and the problem of filters turning very dark did not exist when I started using this product

I have been using this product for sometime, and the problem of filters turning very dark did not exist when I started using this product

Jul 02, 2009 | 3M Filtrete Ultra Allergen Air Filter...

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As for pixel damage from electric fluctuations? That's a load of ****. I've ran so many LCD's and you don't even want to know HOW bad my power fluctuates where I live. I'm talking anywhere from 97v to 130v. Never had a single problem.

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Hope this helps solve your question there buddy. If you have any other questions, please feel free to ask! Don't forget to rate the solution also! Cheers!

As for pixel damage from electric fluctuations? That's a load of ****. I've ran so many LCD's and you don't even want to know HOW bad my power fluctuates where I live. I'm talking anywhere from 97v to 130v. Never had a single problem.

Another good idea however, a UPS. Having a UPS will definitely be a good thing for it and any other electronics such as a gaming system, expensive HD players, and home theaters. A good company to look at is APC Power Products. They make some really good UPS's and it's definitely worth looking into investing into one. These units not only help stabilize bad fluctuations, but also protect from surges and even keep things like movies from being shut off during those small electric power outs that like to reset microwave clocks. You can use one unit for all of your electronics and it's definitely a wise investment for the protection for your TV and periphrials. :)

Hope this helps solve your question there buddy. If you have any other questions, please feel free to ask! Don't forget to rate the solution also! Cheers!

Aug 27, 2008 | Samsung LN-T4061F 40 in. LCD HDTV

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Apr 21, 2008 | Electronics - Others

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