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# Simplification watch

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1. I'm really stuck on this one, any ideas?

(N+500) (1-3N)

Cheers

-----------------------------
Mark
2. Multiplied out you get N-3N^2+500-1500N, which simplifies to 3N^2+1499N-500=0. Then just use the
quadratic formula N= [-b (plus or minus) sqrt(b^2-4ac)]/2a, where a b and c are 3, 1499 and -500.
You should get 1/3 and -500
3. Mark <[email protected]> wrote in uk.education.maths:
[q1]>I'm really stuck on this one, any ideas?[/q1]
[q1]>[/q1]
[q1]>[/q1]
[q1]>(N+500) (1-3N)[/q1]

Multiply it out. A common mnemonic is "FOIL", meaning First, Outside, Inside, Last -- which reminds
you to multiply all possible pairs of terms. Using "FOIL" you have

N - 3N^2 + 500 -1500N

Then collect similar terms (like terms):

-3N^2 - 1499N + 500
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com/ "What in
heaven's name brought you to Casablanca?" "My health. I came to Casablanca for the waters." "The
waters? What waters? We're in the desert." "I was misinformed."
4. In article <[email protected] b-fd.aol.com>, Daniel25386 <[email protected]> wrote:
[q1]>Multiplied out you get N-3N^2+500-1500N, which simplifies to 3N^2+1499N-500=0. Then just use the[/q1]
[q1]>quadratic formula N= [-b (plus or minus) sqrt(b^2-4ac)]/2a, where a b and c are 3, 1499 and -500.[/q1]
[q1]>You should get 1/3 and -500[/q1]

I don't think he wanted to solve the equation (n+500)(3n-1)=0, but in any case, multiplying out and
using the quadratic formula has to be just about the worst possible way to get the right answer.

If (n+500)(1-3n)=0, then either n+500=0, i.e. n=-500, or 1-3n=0, i.e. n=1/3.

That said, I don't know what the original poster *did* want, since I'm hard put to make
(n+500)(1-3n) any 'simpler'.

Just to get slightly on-topic:

<peeve> The use of 'simplify' in a student exercise is a Bad Thing. Which of two equivalent
expressions is 'simpler' is impossible to say in general, and which is more useful depends on the
context. </peeve>

--
Rob. http://www.mis.coventry.ac.uk/~mtx014/
5. Stan Brown <[email protected]> wrote:
[q1]>Mark <[email protected]> wrote in uk.education.maths:[/q1]
[q2]>>I'm really stuck on this one, any ideas? (N+500) (1-3N)[/q2]
[q1]>Multiply it out. -3N^2 - 1499N + 500[/q1]

Personally, I think that that has complicated the expression, not simplified it.
--
Rob. http://www.mis.coventry.ac.uk/~mtx014/
6. Robert Low <[email protected] ac.uk> wrote in uk.education.maths:
[q1]><peeve> The use of 'simplify' in a student exercise is a Bad Thing. Which of two equivalent[/q1]
[q1]>expressions is 'simpler' is impossible to say in general, and which is more useful depends on the[/q1]
[q1]>context. </peeve>[/q1]

Hear, hear!

Which is simpler, (x-1)^-4 or 1/(x-1)^4 ? x^4 - 4x^3 + 6x^2 - 4x + 1 or (x-1)^4 ?

I like to see clearer terms on exams, such as "multiply out" or "express as a sum or difference of
trig functions" or "simplify (no negative or fractional exponents)".

--
Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com/ "What in
heaven's name brought you to Casablanca?" "My health. I came to Casablanca for the waters." "The
waters? What waters? We're in the desert." "I was misinformed."
7. [q1]>A common mnemonic is "FOIL"[/q1]

That's fine, but not as much fun as 'Grinny Gorilla' !! My pupils are trained to spot him... and
they always draw in his two eyebrows, nose and mouth to help them see which terms to multiply.

(In 'FOIL' terms it would be F, L for the eyebrows, I for the nose and O for the mouth.)

It's not very formal, but for some reason this makes expanding brackets a little more bearable - and
they seem to remember it better than FOIL, even though the process is identical!

I got 'Grinny Gorilla' from a colleague a few years back - has anyone else heard of him?

Dan.

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