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Q&A #6091

Teachers' Lounge Discussion: Monomials and polynomials

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2005102610:26:20
Subject: Re: Alegbra 1AB

On 2005102520:59:57, nick wrote:
>	
>Im in 7th grade and learning about monomials and polynomials. My
>teacher is great and all, and i do understand, but the way he taught
>it to our class take forever to do the simplest of problems.  I
wanted
>to know the easiest way to simplify an equation where you multiply a
>monomial by a monomial, a monomial by a polynomial, and especially a
>polynomial by a polynomial.    Thanks a bunch!!!
>
>
>                                          :)Nick:)
>


How about (a+b)(c+d)
You can multiply a times every term in the second polynomial then do
the same thing with b:

ac+ad+bc+bd.  That is the way I usually do it:

But you can use the distributive law:

Multiply the first binomial times every term in the second binomial:

(a+b)c + (a+b)d= ac + bc + ad+bd.

Either way, you get the same answer after rearranging terms. 

You can use either method to do the same for trinomials.  Just a few
more terms to confuse you, possibly.

You can make up polynomial you know the answer to if you have trouble:

(1+2+3+4)(2 + 3 +7)  = 10x12.  One can see the answer is 120.

Using * for multiply:
1*2 + 1*3+1*7 + 2*2+2*3+2*7 +3*2+3*3+3*7+4*2+4*3+4*7 
2 + 3 + 7 + 4 + 6 +14 +6+9 +21 +8 +12 +28 =120

I only made to mistakes that I had to correct.

As you  can see, I didn't have much to do today. 

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