Difference of understanding expressions

Probability · Jul 18, 2013

My tutor previous gave an answer to a question I did and I cannot see how the tutors answer can be right, but I do stand to be corrected on this. I have the following expression. (1 - u)(2u + 1/3). I worked it out and got the answer = 5u / 3 + 1/3 My tutor thinks the answer is - 2u^2 + 5u / 3 + 1/3. I cannot for the like of me see how he can re-introduce - 2u^2 into the expression when it has already been used as 4u? I would really like to show the working out but for some odd reason this forum won't ley me do line breaks? Sorry for the presentation but something is not working correctly otherwise I would show the working out.

Deleted member 4993 · Jul 18, 2013

Probability said:
My tutor previous gave an answer to a question I did and I cannot see how the tutors answer can be right, but I do stand to be corrected on this. I have the following expression. (1 - u)(2u + 1/3). I worked it out and got the answer = 5u / 3 + 1/3 My tutor thinks the answer is - 2u^2 + 5u / 3 + 1/3. I cannot for the like of me see how he can re-introduce - 2u^2 into the expression when it has already been used as 4u? I would really like to show the working out but for some odd reason this forum won't ley me do line breaks? Sorry for the presentation but something is not working correctly otherwise I would show the working out.

Can you perform the following operation:

(a + b) * (c + d) = ?

stapel · Jul 18, 2013

Probability said:
I have the following expression. (1 - u)(2u + 1/3).

This, having grouping symbols, is clearly meant to mean:

. . . . .\(\displaystyle (1\, -\, u)\left(2u\, +\, \dfrac{1}{3}\right)\)

However:

Probability said:
I worked it out and got the answer = 5u / 3 + 1/3 My tutor thinks the answer is - 2u^2 + 5u / 3 + 1/3.

As posted, these mean the below:

. . . . .\(\displaystyle \dfrac{5u}{3}\, +\, \dfrac{1}{3}\)

. . . . .\(\displaystyle -2u^2\, +\, \dfrac{5u}{3}\, +\, \dfrac{1}{3}\)

Are these correct?

Probability said:
I cannot for the like of me see how he can re-introduce - 2u^2 into the expression when it has already been used as 4u?

Um... what?

JeffM · Jul 18, 2013

Probability said:
My tutor previous gave an answer to a question I did and I cannot see how the tutors answer can be right, but I do stand to be corrected on this. I have the following expression. (1 - u)(2u + 1/3). I worked it out and got the answer = 5u / 3 + 1/3 My tutor thinks the answer is - 2u^2 + 5u / 3 + 1/3. I cannot for the like of me see how he can re-introduce - 2u^2 into the expression when it has already been used as 4u? I would really like to show the working out but for some odd reason this forum won't ley me do line breaks? Sorry for the presentation but something is not working correctly otherwise I would show the working out.

\(\displaystyle (1 - u)\left(2u + \dfrac{1}{3}\right) =\)

\(\displaystyle 1 * \left(2u + \dfrac{1}{3}\right) - u * \left(2u + \dfrac{1}{3}\right)=\)

\(\displaystyle 2u + \dfrac{1}{3} - u * \left(2u + \dfrac{1}{3}\right) =\)

\(\displaystyle 2u + \dfrac{1}{3} - 2u^2 - \left(u * \dfrac{1}{3}\right) =\)

\(\displaystyle -2u^2 + u\left(2 - \dfrac{1}{3}\right) - \dfrac{1}{3} =\)

\(\displaystyle -2u^2 + u\left(\dfrac{6}{3} - \dfrac{1}{3}\right) - \dfrac{1}{3} =\)

\(\displaystyle -2u^2 + \dfrac{5u}{3} - \dfrac{1}{3}.\)

Lets see if it checks out if u = 1/4.

\(\displaystyle \left(1 - \dfrac{1}{4}\right)\left(2 * \dfrac{1}{4} + \dfrac{1}{3}\right) = \dfrac{3}{4} * \left(\dfrac{1}{2} + \dfrac{1}{3}\right) = \dfrac{3}{4} * \dfrac{5}{6} = \dfrac{5}{8}.\)

\(\displaystyle - 2\left(\dfrac{1}{4}\right)^2 + \dfrac{5 * \dfrac{1}{4}}{3} + \dfrac{1}{3} = \left(- 2 * \dfrac{1}{16}\right) + \dfrac{5}{12} + \dfrac{1}{3} = - \dfrac{1}{8} + \dfrac{5}{12} + \dfrac{1}{3} = -\dfrac{3}{24} + \dfrac{10}{24} + \dfrac{8}{24} =\dfrac{15}{24} = \dfrac{5}{8}. \)

Your tutor is right as you would have seen if you had worked out an example.

Probability · Jul 19, 2013

JeffM said:
\(\displaystyle (1 - u)\left(2u + \dfrac{1}{3}\right) =\)

\(\displaystyle 1 * \left(2u + \dfrac{1}{3}\right) - u * \left(2u + \dfrac{1}{3}\right)=\)

\(\displaystyle 2u + \dfrac{1}{3} - u * \left(2u + \dfrac{1}{3}\right) =\)

\(\displaystyle 2u - \dfrac{1}{3} - 2u^2 - \left(u * \dfrac{1}{3}\right) =\)

\(\displaystyle -2u^2 + u\left(2 - \dfrac{1}{3}\right) - \dfrac{1}{3} =\)

\(\displaystyle -2u^2 + u\left(\dfrac{6}{3} - \dfrac{1}{3}\right) - \dfrac{1}{3} =\)

\(\displaystyle -2u^2 + \dfrac{5u}{3} - \dfrac{1}{3}.\)

Lets see if it checks out if u = 1/4.

\(\displaystyle \left(1 - \dfrac{1}{4}\right)\left(2 * \dfrac{1}{4} + \dfrac{1}{3}\right) = \dfrac{3}{4} * \left(\dfrac{1}{2} + \dfrac{1}{3}\right) = \dfrac{3}{4} * \dfrac{5}{6} = \dfrac{5}{8}.\)

\(\displaystyle - 2\left(\dfrac{1}{4}\right)^2 + \dfrac{5 * \dfrac{1}{4}}{3} + \dfrac{1}{3} = \left(- 2 * \dfrac{1}{16}\right) + \dfrac{5}{12} + \dfrac{1}{3} = - \dfrac{1}{8} + \dfrac{5}{12} + \dfrac{1}{3} = -\dfrac{3}{24} + \dfrac{10}{24} + \dfrac{8}{24} =\dfrac{15}{24} = \dfrac{5}{8}. \)

Your tutor is right as you would have seen if you had worked out an example.

Thanks Jeff, I can follow what you have done to the fourth line, but don't understand how or why the arithmetic symbols have changed signs in each part to continue.

My tutor did not work by example which is why I am struggling with this, is there a simpler method to explain than above please?

Deleted member 4993 · Jul 19, 2013

Probability said:
Thanks Jeff, I can follow what you have done to the fourth line, but don't understand how or why the arithmetic symbols have changed signs in each part to continue.

My tutor did not work by example which is why I am struggling with this, is there a simpler method to explain than above please?

You did not respond to my question posed some time ago.

Can you simplify the following:

(a + b) * (c + d)

also try

(a - b ) * ( c - d)

Secondly I suggest that you should copy the solution given by Jeff - line by line.

JeffM · Jul 19, 2013

Probability said:
Thanks Jeff, I can follow what you have done to the fourth line, but don't understand how or why the arithmetic symbols have changed signs in each part to continue.

My tutor did not work by example which is why I am struggling with this, is there a simpler method to explain than above please?

Sorry. I made a typographical error in the fourth line and did not catch it in my editing. I will now fix my original post.

The fourth line should read \(\displaystyle 2u + \dfrac{1}{3} - 2u^2 - \left(u * \dfrac{1}{3}\right)\).

Are you good now?

And answer Subhotosh Khan's questions: they will help you forever

mmm4444bot · Jul 19, 2013

Probability said:
My tutor did not work by example

is there a simpler method

There's a method called FOIL, but it's not simpler, really ... the multiplications are done in different order; you still need to combine like-terms. Practice! :cool:

lookagain · Jul 20, 2013

JeffM;339043 Lets see if it checks out if u = 1/4. [tex said:
- 2\left(\dfrac{1}{4}\right)^2 + \dfrac{5 * \dfrac{1}{4}}{3} + \dfrac{1}{3} = \left(- 2 * \dfrac{1}{16}\right) + \dfrac{5}{12} + \dfrac{1}{3} = - \dfrac{1}{8} + \dfrac{5}{12} + \dfrac{1}{3} = -\dfrac{3}{24} + \dfrac{10}{24} + \dfrac{8}{24} =\dfrac{15}{24} = \dfrac{5}{8}. [/tex]\(\displaystyle \ \ \ \ \ \) <----- That check of u = 1/4 is not sufficient. Neither is it sufficient for two different values of the variable u to wind up checking between those expressions. *Three* different values of the variable u must check out in order to state as a surety that a quadratic expression is equivalent to another quadratic expression. In a related idea, three distinct points in the plane determine a unique parabola.

Your tutor is right as you would have seen if you had worked out an example.

Probability said:
. I have the following expression. (1 - u)(2u + 1/3). I worked it out and got the answer = 5u / 3 + 1/3 My tutor thinks the answer is - 2u^2 + 5u / 3 + 1/3.

\(\displaystyle \ \ \ \)Compare checking u = 0 in the expressions of the OP's quote box. Each side equals 1/3 when u = 0 is checked, but those two expressions are not equivalent to each other.

Probability · Jul 20, 2013

Subhotosh Khan said:
You did not respond to my question posed some time ago.

Can you simplify the following:

(a + b) * (c + d)

also try

(a - b ) * ( c - d)

Secondly I suggest that you should copy the solution given by Jeff - line by line.

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

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

This demonstrates that FOIl is understood, but does not show how Jeff actually changed the arithmetic signs within the terms of use of FOIL, i.e.

(1 - u) * (2u + 1/3) = 2u + 1/3 - 2u^2 - u/3

From this point inwards is where different methods must be available to solve this expression because the method I used does not provide the full solution!

Jeff wrote;

(1 - u) * (2u + 1/3) = 2u + 1/3 - u * (2u + 1/3)

Which Jeff then says goes onto;

2u + 1/3 - 2u^2 - (u * 1/3)

Is this last line actually correct?

Can you now introduce another u and changed the arithmetic sign from + 1/3 inside the bracket to * meaning multiplying it?

I can see now reading through the replies this expression is not quite as clear as it first may appear to be?

Deleted member 4993 · Jul 20, 2013

Probability said:
(a + b) * (c + d) = ac + ad + bc + bd

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

This demonstrates that FOIl is understood, but does not show how Jeff actually changed the arithmetic signs within the terms of use of FOIL, i.e.

(1 - u) * (2u + 1/3) = 2u + 1/3 - 2u^2 - u/3

From this point inwards is where different methods must be available to solve this expression because the method I used does not provide the full solution!

Jeff wrote;

(1 - u) * (2u + 1/3) = 2u + 1/3 - u * (2u + 1/3) .... Work it out with paper and pencil .... if we have to write every step, it will take us for ever to answer a question

(1-u) * (2u + 1/3)

= (1) * (2u + 1/3) + (-u) * (2u + 1/3)

= (1) * (2u) + (1) * (1/3) + (-u) * (2u) + (-u) * (1/3)

= 2u + 1/3 + (-2u²) + (-u/3)

= 2u + 1/3 - 2u² - (u/3)

These are some of the intermediate steps - you are supposed to work this out

Which Jeff then says goes onto;

2u + 1/3 - 2u^2 - (u * 1/3)

Is this last line actually correct?

Can you now introduce another u and changed the arithmetic sign from + 1/3 inside the bracket to * meaning multiplying it?

I can see now reading through the replies this expression is not quite as clear as it first may appear to be?

.

Deleted member 4993 · Jul 20, 2013

Probability said:
You have done these CORRECTLY

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

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

Now think how come you have (-b) and (-d) but after multiplication you got (+bd)

This demonstrates that FOIl is understood, but does not show how Jeff actually changed the arithmetic signs within the terms of use of FOIL, i.e.

(1 - u) * (2u + 1/3) = 2u + 1/3 - 2u^2 - u/3 ....................................................... (1)

From this point inwards is where different methods must be available to solve this expression because the method I used does not provide the full solution!

Jeff wrote;

(1 - u) * (2u + 1/3) = 2u + 1/3 - u * (2u + 1/3)

Which Jeff then says goes onto;

2u + 1/3 - 2u^2 - (u * 1/3)..................................................................(2)

(1) and (2) are mathematically same because

- (u * 1/3) = -(u/3) = - u/3

Just like

- (2 * 1/3) = -(2/3) = - 2/3

Is this last line actually correct? only

Can you now introduce another u and changed the arithmetic sign from + 1/3 inside the bracket to * meaning multiplying it?

I can see now reading through the replies this expression is not quite as clear as it first may appear to be?

.

Probability · Jul 21, 2013

Subhotosh Khan said:
.

I understand the arithmetic - + - = +.

The problem is not FOIL as some may think, but a lack of experience in understanding the different techniques and ideas used in algebra, which to more experienced people they can't see it from the learners point of view.

I now understand that Jeff "my words" factored out u from 2u to end up with - 2u^2 - (u * 1/3)

I don't think understanding FOIL will learn a student the above, this is experience beyond a book in what Jeff had done.

mmm4444bot · Jul 21, 2013

Probability said:
I don't think understanding FOIL will learn a student the above

What is "the above"? Multiplying two binomials together?

FOIL is not intended to explain JeffM's method. It's just one algorithm for multiplying two binomials; there are others...

I understand the arithmetic - + - = +

You understand, but I think you're expressing the arithmetic above wrongly.

A negative TIMES a negative is a positive, but a negative PLUS a negative is still a negative. :cool:

Difference of understanding expressions

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