Maths help please...? Algebra. Grade - D

Erm... I'm slightly confused.. on this Question. And I was wondering if someone would be able to help me understand please?

So I had to simplify this Algebraic Expression - 7ab + 3ba

The ANS is 10ab. Which I don't understand why. Could someone please explain? What I don't understand is that there is 2 a's and 2 b's but when they simplified your not able to tell that their is two a's and two b's.

Thanks in advance xx

Original post by Carrot_Cake_13

Erm... I'm slightly confused.. on this Question. And I was wondering if someone would be able to help me understand please?

So I had to simplify this Algebraic Expression - 7ab + 3ba

The ANS is 10ab. Which I don't understand why. Could someone please explain? What I don't understand is that there is 2 a's and 2 b's but when they simplified your not able to tell that their is two a's and two b's.

Thanks in advance xx

I am assuming that is 7ab not -7ab as it reads!

If you have 7 of something and add 3 more then you get 10 of it.

ab = ba because the order of multiplication does not matter*.

* Anyone who mentions matrices here deserves a punch.

(edited 10 years ago)

Reply 2

Doglamlico

16

Original post by Carrot_Cake_13

Erm... I'm slightly confused.. on this Question. And I was wondering if someone would be able to help me understand please?

So I had to simplify this Algebraic Expression - 7ab + 3ba

The ANS is 10ab. Which I don't understand why. Could someone please explain? What I don't understand is that there is 2 a's and 2 b's but when they simplified your not able to tell that their is two a's and two b's.

Thanks in advance xx

If you think about multiplication,

3 \times 4 = 12

is the same as

4 \times 3 = 12

.

In the same way, since

a

and

b

just represent numbers,

a \times b = b \times a

, or

ab = ba

So we can rewrite the expression

7ab + 3ba

as

7ab + 3ab

.

Now we have

7(ab) + 3(ab)

which if you carry out the addition, gives

10ab

.

(edited 10 years ago)

Reply 3

Phichi

11

Original post by Carrot_Cake_13

Erm... I'm slightly confused.. on this Question. And I was wondering if someone would be able to help me understand please?

So I had to simplify this Algebraic Expression - 7ab + 3ba

The ANS is 10ab. Which I don't understand why. Could someone please explain? What I don't understand is that there is 2 a's and 2 b's but when they simplified your not able to tell that their is two a's and two b's.

Thanks in advance xx

7ab+3ba = 10ab

Its like

7ax+3xa = 7(a)(x)+3(a)(x) = 10ax

Original post by The Polymath

...

You can get the multiplication sign in LaTeX by using \times. Using this symbol would make your post less confusing.

Edit: You already know!

Reply 5

Doglamlico

16

Original post by Mr M

You can get the multiplication sign in LaTeX by using \times. Using this symbol would make your post less confusing.

Edit: You already know!

I'm a little rusty :colondollar:

Thanks though :yy:

Reply 6

Carrot_Cake_13

OP

17

Original post by The Polymath

Now we have

7(ab) + 3(ab)

which if you carry out the addition, gives

10ab

.

Okay I'm fine with everything you explained up until the last sentence...

So...I understand to simplify you need to add the 7+3 which gives us the 10.
But if you add the ab + ba... Does it not give us 2 a's and 2 b's.
Yet in the answer there is only one a and one b represented - 10ab

I don't know if anything I said ^^ makes sense :/

Reply 7

Doglamlico

16

Original post by Carrot_Cake_13

Okay I'm fine with everything you explained up until the last sentence...

So...I understand to simplify you need to add the 7+3 which gives us the 10.
But if you add the ab + ba... Does it not give us 2 a's and 2 b's.
Yet in the answer there is only one a and one b represented - 10ab

I don't know if anything I said ^^ makes sense :/

We got to

7ab + 3ab

, which I'm assuming you're okay with.

So you start with 7 lots of (ab), add 3 lots of (ab), which gives you 10 lots of (ab).

The key here is to just think of

ab

as a number.

a

might be 2,

b

might be 6, and

ab

would therefore be 12.

(7 lots of 12) + (3 lots of 12) gives you (10 lots of 12).

Reply 8

Kvothe the Arcane

20

Original post by Carrot_Cake_13

Okay I'm fine with everything you explained up until the last sentence...

So...I understand to simplify you need to add the 7+3 which gives us the 10.
But if you add the ab + ba... Does it not give us 2 a's and 2 b's.
Yet in the answer there is only one a and one b represented - 10ab

I don't know if anything I said ^^ makes sense :/

it's 7 lots of ab plus 3 lots of ab giving you 10 lots of ab.
Edit: You have got to be kidding me.

Reply 9

Carrot_Cake_13

OP

17

Original post by The Polymath

We got to

7ab + 3ab

, which I'm assuming you're okay with.

So you start with 7 lots of (ab), add 3 lots of (ab), which gives you 10 lots of (ab).

The key here is to just think of

ab

as a number.

a

might be 2,

b

might be 6, and

ab

would therefore be 12.

(7 lots of 12) + (3 lots of 12) gives you (10 lots of 12).

Ohmygossh.... Hehehehe thank you :biggrin:

I'm feeling very erm... Stupid now :blushing:

Reply 10

james22

16

Original post by Carrot_Cake_13

Okay I'm fine with everything you explained up until the last sentence...

So...I understand to simplify you need to add the 7+3 which gives us the 10.
But if you add the ab + ba... Does it not give us 2 a's and 2 b's.
Yet in the answer there is only one a and one b represented - 10ab

I don't know if anything I said ^^ makes sense :/