Question

simplify: a+b+3a^2 -3b^2

Answer 1

think back to your previous question, remember I showed you that:\[a^2-b^2=(a+b)(a-b)\]

Answer 2

yeah but Hw do I use it to this?

Answer 3

look at the last two terms in your equation - factor out the 3 and what will you get?

Answer 4

3(a^2 -b^2)

Answer 5

now can you spot anything?

Answer 6

ok @Anikate back to your question

Answer 7

ok
:)

Answer 8

so you factored out a 3 from the last two terms to get: \(3(a^2-b^2)\)
Can you now spot how to factorise this?

Answer 9

ummm...

Answer 10

look at my first reply to this question above ^^^

Answer 11

a+b+3(a+b)(a-b)
I think?

Answer 12

perfect!
now you see you have (a+b) at the start of this expression, and also (a+b) in the term 3(a+b)(a-b)

Answer 13

so you should be able to factor out the (a+b)

Answer 14

which one?

Answer 15

both

Answer 16

could u plz show me how? I am not so bright...

Answer 17

imagine you had: x + 3xy
you could factor out the x to get: x(1+3y)

Answer 18

now just think of the 'x' as being 'a+b'

Answer 19

huh?

Answer 20

you have: a+b + 3(a+b)(a-b)
which we can write as: (a+b) + 3(a+b)(a-b)

think of the (a+b) term as being a single number, say 'x', and factor it out

Answer 21

how would you factor out the 'x' in: x + 3x(a-b)

Answer 22

um where did u go?

Answer 23

I was waiting for you to reply.

Answer 24

I was confused a bit?

Answer 25

3(2a+2b)(a-b)?

Answer 26

sry 2 keep u waiting

Answer 27

remember I cannot see you - so on sites like this it is important to give feedback via chat otherwise it is very difficult to help.

Answer 28

sry

Answer 29

so, my last question to you was:

how would you factor out the 'x' in: x + 3x(a-b)

Answer 30

3(2a+2b)(a-b)

Answer 31

plz read my question carefully - your answer should contain an 'x' in it:

how would you factor out the 'x' in: x + 3x(a-b)

Answer 32

4x(a-b)

Answer 33

ok - I see where you are confused now

Answer 34

ok

Answer 35

what you did was the correct factorisation of: x(a-b) + 3x(a-b)

Answer 36

what we have is: x + 3x(a-b)

think of this as 'x' times one, plus 'x' times 3(a-b)

Answer 37

k right now on the paper I am at a+b+3(a+b)(a-b)

Answer 38

4x(a-b)

Answer 39

that is also wrong

Answer 40

\[a+b+3(a+b)(a-b) = (a+b)\times1+(a+b)\times3(a-b)\]

Answer 41

if we now pull out the (a+b) terms, we end up with:\[(a+b)(1+3(a-b))\]

Answer 42

does that make sense to you?

Answer 43

umm.. no