use foil to solve (5x+3+3y) (5x+4)

[bob]

can you please help me with the following question ,
I have to use ,,,,,foil ,,,,, to solve

The question is (5x+3+3y) (5x+4)

thanks

 

[Loren]

Re: help

It is my understanding that FOIL may be used when multiplying a binomial times a binomial. You have stated a trinomial times a binomial. If you must use FOIL, one approach would to combine two terms. Here's an example...
(3x+2+4y)(3x+7)=
([3x+2]+4y)(3x+7)=
F is [3x+2]*3x = 9x^2 + 6x
O is [3x+2]*7 = 21x + 14
I is 4y*3x = 12xy
L is 4y*7 = 28y
Put them all together getting 9x^2 + 6x + 21x + 14 + 12xy + 28y then simplify by gathering like terms.

 

[bob]

Re: help

thank you very much

 

[stapel]

I have to use ,,,,,foil ,,,,, to solve (5x+3+3y) (5x+4)

Since this is an expression, not an equation (since there is no "equals" sign), your book should not have told you to "solve" this. There is nothing to solve here; all you can do is simplify.

Also, since the "FOIL" method works only for multiplying two binomials, and yet your book and/or instructor told you to use "FOIL" for a product to which it quite-clearly does not apply, you will need lessons (to replace what your instructor and book don't know) on how to multiply polynomials the normal way (which will also cover the multiplication of two binomials).

Unfortunately, we cannot here replace the lessons you're not getting in your class, so you may want to try some of the many great online lessons available. :idea:

. . . . .Google results for "multiplying polynomials"

Good luck!

Eliz.

 

[nycfunction]

can you please help me with the following question ,
I have to use ,,,,,foil ,,,,, to solve

The question is (5x+3+3y) (5x+4)

thanks

I will pick up where Loren ended her reply.

Loren said:

"Put them all together getting 9x^2 + 6x + 21x + 14 + 12xy + 28y then simplify by gathering like terms."

We have this polynomial:

9x^2 + 6x + 21x + 14 + 12xy + 28y.

We combine like terms to complete the problem.

So, what can I add?

How about 6x + 21x?

Then, 6x + 21x = 27x.

Is there anything else I can combine?

No, right?

The final answer is:

9x^2 + 27x + 14 + 12xy + 28y

 

[stapel]

You've been given the complete solution to copy into your homework for this exercise. However, copying down one solution is not, in general, going to be helpful (for instance, on tests, where you'll have to do the multiplication yourself). :shock:

So, for your own sake, please do study some online lessons, and learn how to do this on your own! :wink:

Eliz.

 

[jwpaine]

I know it has already been stated (multiple times) but it is important to remember that every term needs to be multiplied with every other term. Think of it like doing "cheers" with glasses at a table.

(a + b + c)(d + e) = d(a + b + c) + e(a + b + c) = da + db + dc + ea + eb + ec

See how d(a + b + c) + e(a + b + c) can be factored back into (a + b + c)(d + e) ?

Example: (a + b)(a + b) : think of the first binomial as a variable, u, so you have u(a + b), distributing in that u, you get ua + ub, thus you have a(a+b) + b(a + b) which you can then distribute the a and b into each binomial to give you a^2 + 2ab + b^2

Try not to get stuck on the "First, outside, inside, last" phrase, just think of it as factoring once and then distributing terms to give you your end expansion.


Cheers,
John

 

[kasie-tutor]

:lol: You know you're a mathematician when you take what people say literally. :lol: If you tell a mathematician that you didn't write out your steps because it was pointless, they'ld say, "Oh, you want to use my pencil sharpener?"

When you tell a mathematician you need to FOIL a trinomial and a binomial, they will take you literally and turn the trinomial into a binomial by combining two of its terms. Then you can FOIL. :lol:

I think most students use the term FOIL when they just mean "multiply" and "solve" when they mean "find the answer."

~Kasie

 

[stapel]

I think most students use the term FOIL when they just mean "multiply" and "solve" when they mean "find the answer."

Students might know what they're pretty sure they really meant, but when they use specific terms in specific ways, the listener can hardly be faulted for taking them at their word. :wink:

In my (admittedly limited) experience, when a student says "FOIL", he mean exactly that: the application of the one algorithm that he learned for multiplying binomials, but which he thinks must be the process for multiplying all polynomials. This very common mistaken understanding has led many instructors nowadays to strive to avoid "FOIL". It seems to cause more problems than it solves. :shock:

(I can't think of a time when a student ever said "solve by FOIL" but really meant "simplify the product of these non-binomials, and yes, I understand the difference." In fact, a great proportion of the questions which arise regarding "FOIL" are precisely what was seen here: The student thinks that "FOIL" is all there is to multiplying any two polynomials, and has no idea how to approach the simplification of the product of anything other than two binomials.)

While math helpers might indeed be needlessly and overly literal (an assumption I do not assert), the alternative seems generally to work rather less well. Trying to read a student's mind, making assumptions regarding what he "really" meant, is naturally fraught with error, and answering the question that one has decided that the student really meant to ask-- well, it generally just ticks the student off. :evil:

Mathematics is a literal process, pretty much by definition. And students aren't usually looking to get "a discussion in the same general topic area", but the exact and literal value to an exact and literal exercise. When there is confusion regarding the question statement, it seems (to me) generally to be most helpful, in order to provide the literal help requested, to determine the literal meaning of the post. And, as in this case, when a student states that he is required to use a particular method in a situation to which that method does not apply, it seems only reasonable (and fair to the student) to point out the potential problem, and to attempt clarification.

The above is just my opinion, of course; I could be wrong....

Eliz.

 

[kasie-tutor]

My inner math dork is coming out. Please Excuse My Dear Inner Math Dork. Order of Operations: Explain "FOIL" and "solve" and ask for clarification; Meanwhile offer help assuming student meant what they said as done professionally above.

Don't be foiled by FOIL. It is a mnemonic for the special case of binomial times binomial.

When you tell a really good mathematician you need to FOIL a trinomial and a binomial, they will take you literally and turn the trinomial into a binomial by combining two of its terms.

Respectable AND humorous. Math is fun AND precise.

\(\displaystyle \clubsuit\) Kasie

 

[tkhunny]

...and FOIL is foilish. Get rid of it and simply learn to multiply.

 

[stapel]

...and FOIL is foilish. Get rid of it and simply learn to multiply.

I have to agree. Teaching "FOIL" as though it were all there is to the topic is much like teaching a child one of the "trick" methods for remembering the "times nines" (such as using one's fingers), and then expecting the student to figure out, on his own, that none of the other "timeses" works that way, and requiring him to teach himself the normal way of multiplication for the "times ones" through the "times eights".

It's hard to fault the student for being utterly confused. :shock: And I would certainly hope that any caring adult in the student's world would point out the error and provide instruction in the general (and more helpful) methods.

Again, this is only my (perhaps "too literal") opinion; I could be wrong....

Eliz.