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Problem Solving Made Easy (8th Grade)#5: How to find the Product of two Binomials using FOIL Method? by fabio2614

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Problem Solving Made Easy (8th Grade)#5: How to find the Product of two Binomials using FOIL Method?
<center>https://image.ibb.co/eiyqFJ/p11.png</center>
<center><sub>How to find the product of two binomials using FOIL Method?</sub></center>
<center><h4>"Solving math problem the easier way is intended to help students discover that learning math is easy. Be inspired and motivated with the hope it can sway them from having neutral opinions about math to liking it."</h4></center>

Hello steemian friends! Today's post discusses the steps on " How to find the Product of two Binomials using FOIL Method". Again, I made it sure that the language used in the presentation is user-friendly in the sense that it is easily understood by a reader who has at least an 8th-grade education (age 13-14).

In my 8<sup>th</sup> grader's classes, I did emphasize that there are many ways on how to find the product of two binomials. If the task is to square a binomial then the use of a pattern is the easiest and the shortest. One can even mentally do it since the answer is readily seen. (Yet only if one had mastered the operations on polynomials and the laws of exponent in finding its product.).

To my surprise!, most of my regular classes (regular class because we have a Science class and a Pilot class who are homogeneous and are fast learners.) feel comfortable in using the FOIL method in finding the product of two binomials even if it is a "Special Product". At times when I strictly imposed to them to only follow the pattern (since it is easier and shorter on special product) Nah! most of them failed.  So I need to look for another strategy, to somewhat meet them halfway (the one that would make the majority happy...haha!) And that is to let them used either method provided that we will arrive at the same answer. Alrigth, game!

<h3>What is FOIL method? - brief review</h3>
**FOIL** is just a mnemonic for the standard method of multiplying two binomials.
>F - means product of the first terms
 O - means product of the outer terms
  I  - means product of the inner terms
  L - means product of the last terms

So to apply this method, we need to recall first on the following.
 <center><h4>*So here!*</h4></center>
<center>Let **( a + b )**  and **( c + d )** be the two binomials, where,</center>
<center>https://image.ibb.co/cA1t2y/p1.png</center>

<center><h4>For the location of the " Inner " and " Outer" terms, we have:</h4>
https://image.ibb.co/dFRwpd/p2.png</center>

<h3>How to find the product of two binomials using FOIL method?</h3>
Let **( a + b )**  and **( c + d )** be the two binomials.

<h4>Here are the steps:</h4>
- Step 1. Find the product of the first terms ( **F** )
>https://image.ibb.co/iEMFXy/p4.png
- Step 2. Find the product of the outer terms ( **O** )
>https://image.ibb.co/mCgXCy/p6.png
- Step 3. Find the product of the inner terms ( **I** )
>https://image.ibb.co/hu48kJ/p7.png
- Step 4. Find the product of the last terms ( **L** )
>https://image.ibb.co/hSYR5J/p9.png

Putting them together we have,
https://image.ibb.co/e1YLXy/p11.png

<h3>Application:</h3>

---------------
<h4>Problem:</h4> *Find the product of **(3x +6 )(x+5)**.*
<h4>Solution:</h4>
- Step 1. Find the product of the first terms ( **F** )
>https://image.ibb.co/iErJKd/p12.png
- Step 2. Find the product of the outer terms ( **O** )
>https://image.ibb.co/nQMhCy/p13.png
- Step 3. Find the product of the inner terms ( **I** )
>https://image.ibb.co/eLBzsy/p14.png
- Step 4. Find the product of the last terms ( **L** )
>https://image.ibb.co/cdP2Cy/p15.png

Putting them together we have 
https://image.ibb.co/fPuikJ/p16.png

<h3>Conclusion</h3>
Therefore https://image.ibb.co/mHLCed/p17.png

Note: It is important that one should be very careful in combining like terms. Good thing we only used positive integers here. Students usually overlooked signed numbers maybe because they don't have mastery in doing it, or they just got mistake due to carelessness.

So we're done! That's how we find the product of two binomials using **FOIL** method. Thanks for learning with me. Steem on!

-------
References:
[FOIL method](https://en.wikipedia.org/wiki/FOIL_method)
[Binomials](https://en.wikipedia.org/wiki/Binomial)
[Polynomials](https://en.wikipedia.org/wiki/Polynomial)
Work text in Mathematics: e - math8

Images are all mine.

-------
<center>https://image.ibb.co/jnRqXy/resized1.png
<h3>"We live and learn, at any rate we live"</h3>
https://image.ibb.co/muRGpd/resized.png</center>
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@biblegateway · 
God bless you. https://steemit.com/@biblegateway
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@carlitojoshua · 
I really love this topic <3
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@fabio2614 · 
hi dong... you really love math ha😊
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@carlitojoshua · 
Yes, I really do <3 What a great teacher you are maam @fabio2614 I'm sure your students would love math as well :)
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@leeart · 
This is easy to follow and the illustrations helped a lot to make it clearer.  This is going to be helpful to students and parents alike.<br /><br />This comment was made from <a href="https://ulogs.org">https://ulogs.org</a>
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@fabio2614 · 
Definitely that's  really the intention my friend😊 thanks for noticing it.
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@utopian-io · 
#### Hi @fabio2614!

Your post was upvoted by utopian.io in cooperation with steemstem - supporting knowledge, innovation and technological advancement on the Steem Blockchain.

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@fabio2614 · 
wow! thank you so much for the support😊
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@zen-art · 
Good work on creating those images yourself and a great post in general. So nice to have this kind of posts on the platform too. Kudos! 💚
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@fabio2614 · 
Thank you so much for dropping by @zen-art. You are so kind to have said those words😅
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