Hi,
So to factorise this:
24(a+b) b + 153 (a+b)^2
What would be the first step?
Find the HCF for 24 and 153?
How to Simplify this Expression?
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 1
 11102016 12:45
Last edited by Exceptional; 11102016 at 12:54. 
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 2
 11102016 12:52
(Original post by Exceptional)
Hi,
So to factorise this:
24(a+b) b + 153 + (a+b)^2
What would be the first step?
Find the HCF for 24 and 153?
Check your plus signs. 
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 3
 11102016 12:55

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 4
 11102016 12:56
(Original post by Exceptional)
Hi,
So to factorise this:
24(a+b) b + 153 (a+b)^2
What would be the first step?
Find the HCF for 24 and 153? 
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 5
 12102016 20:13
(Original post by RDKGames)
Well the first step would be to take out any common factors you see that the two terms share. 
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 6
 12102016 20:17
(Original post by Exceptional)
3 for 24 and 153. And the a's and b's. Would I need to expand the brackets first before I can factorise the whole thing? 
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 7
 12102016 20:46
(Original post by RDKGames)
Expanding is the opposite of factorising, so no you do not need to expand the brackets. If you treat the bracket (a+b) as whatever number you want, you can see that you can easily factor it out of the whole expression without expansion. 
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 8
 13102016 16:59
(Original post by Exceptional)
Hmm, I've been told a few contradictory methods to solve it. Someone has said that it's necessary to expand and simplify it before factorising it.
Hence write it as:
24b(a+b) + 153(a+b)(a+b)
= (a+b)(24b + 153(a+b))
= 3(a+b)(8b + 51(a+b))
= 3(a+b)(51a + 59b). 
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 9
 16102016 19:04
(Original post by HapaxOromenon3)
Most likely the reason they say that is that they don't fully appreciate that (a+b) is a common factor.
Hence write it as:
24b(a+b) + 153(a+b)(a+b)
= (a+b)(24b + 153(a+b))
= 3(a+b)(8b + 51(a+b))
= 3(a+b)(51a + 59b).
But, I just don't understand the thought process behind it.
How did you know to write '24b(a+b)' from '24(a+b)b'?
Where did '(a+b)' go in 24b(a+b) + 153(a+b)(a+b)' when you got to the next step, '3(a+b)(8b+51(a+b))'?
Lastly, where did you get 59b from?
Basically, I need an explanation because I don't understand how to do this when faced with new problems. 
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 10
 16102016 19:46
(Original post by Exceptional)
Thank you!
But, I just don't understand the thought process behind it.
How did you know to write '24b(a+b)' from '24(a+b)b'?
Where did '(a+b)' go in 24b(a+b) + 153(a+b)(a+b)' when you got to the next step, '3(a+b)(8b+51(a+b))'?
Lastly, where did you get 59b from?
Basically, I need an explanation because I don't understand how to do this when faced with new problems.
Notice that 3(a+b)(8b+51(a+b)) = 3(a+b)(8b) + 3(a+b)(51(a+b)) = 3(8b)(a+b) + 3(51)(a+b)(a+b) etc.
The key idea is that (a+b)^2 = (a+b)(a+b).
8b + 51(a+b) = 8b + 51a + 51b = 51a + 59b.
All of this is basic algebra. 
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 11
 16102016 20:05
(Original post by Exceptional)
Hi,
So to factorise this:
24(a+b) b + 153 (a+b)^2
What would be the first step?
Find the HCF for 24 and 153?
Factorise:
Let us know if you can do this and post your answer. 
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 12
 16102016 21:42
(Original post by notnek)
I think you should try something a bit simpler.
Factorise:
Let us know if you can do this and post your answer. 
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 13
 16102016 21:44
(Original post by HapaxOromenon3)
24*b*(a+b) = 24*(a+b)*b as multiplication is commutative (can be done in any order)
Notice that 3(a+b)(8b+51(a+b)) = 3(a+b)(8b) + 3(a+b)(51(a+b)) = 3(8b)(a+b) + 3(51)(a+b)(a+b) etc.
The key idea is that (a+b)^2 = (a+b)(a+b).
8b + 51(a+b) = 8b + 51a + 51b = 51a + 59b.
All of this is basic algebra. 
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 14
 16102016 21:48
(Original post by Exceptional)
3x(8b + 51x)?
Now compare the question you just did with the original question:
Notice that the difference is that is now . But you can still take out as a factor just like you took out .
Try your original question again with this in mind and see how you go.
A lot of people have trouble with kind of question  you're not the only one. 
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 15
 16102016 21:56
(Original post by notnek)
That's correct.
Now compare the question you just did with the original question:
Notice that the difference is that is now . But you can still take out as a factor just like you took out .
Try your original question again with this in mind and see how you go.
A lot of people have trouble with kind of question  you're not the only one. 
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 16
 16102016 22:22
(Original post by Exceptional)
It's making more sense, but then why isn't the answer 3(a+b)(8b + 51a)? That way you'd get 24 and 153 like in the original question if you tried to expand.
Both have been factorised in exactly the same way. The only difference is that the first one uses and the second uses . 
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 17102016 11:55
(Original post by notnek)
Both have been factorised in exactly the same way. The only difference is that the first one uses and the second uses .
So, is that an acceptable answer? Because others have said the answer is '3(a+b)(51a + 59b)'. 
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 17102016 12:03
(Original post by Exceptional)
Okay, I can see that. Thank you.
So, is that an acceptable answer? Because others have said the answer is '3(a+b)(51a + 59b)'. 
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 19
 17102016 12:13
(Original post by Exceptional)
Okay, I can see that. Thank you.
So, is that an acceptable answer? Because others have said the answer is '3(a+b)(51a + 59b)'.
That;'s where the comes from.
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Updated: October 17, 2016
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