
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 2nd, 2017, 04:24 AM  #1 
Newbie Joined: Jul 2017 From: Earth Posts: 6 Thanks: 1  Need help checking/show method. Factorise a) [check] 6x^2  21xy + 8xz  28yz = 3x(2x  7y) + 4z(2x  6y) b) [method](x  1)^2  (y  2)^2 c) [check] p^2  y^4 = (p + y^2)(p  y^2) d) [method] 16a^2  (3b + 4c)^2 e) [check] 3ax + bx  3ay  by  9a  3b = 3ax  3ay  9a  3b + bx  by = 3(ax  ay  3a  3b) + b(x  y) Last edited by JoKo; August 2nd, 2017 at 04:45 AM. 
August 2nd, 2017, 04:26 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,285 Thanks: 439 Math Focus: Yet to find out. 
What have you tried? Let's start with just one question at a time first..

August 2nd, 2017, 04:55 AM  #3 
Newbie Joined: Jul 2017 From: Earth Posts: 6 Thanks: 1 
Well, for (d) I expanded the bracket and tried to factorise from there; $\displaystyle 16a^2  (3b +4c)^2$ $\displaystyle = 16a^2 + 9b^2 + 24bc + 16c^2$ $\displaystyle = 4(4a^2 + 6bc + 4c^2) + 3(3b^2)$ 
August 2nd, 2017, 06:07 AM  #4  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,285 Thanks: 439 Math Focus: Yet to find out.  Quote:
$ (3b +4c)^2 = (3b + 4c)(3b + 4c) = (9 b^2 + 12bc + 12bc + 16c^2) = 1*(9 b^2 + 24bc + 16c^2) = ( 9 b^2  24bc  16c^2)$  
August 2nd, 2017, 06:32 AM  #5 
Newbie Joined: Jul 2017 From: Earth Posts: 6 Thanks: 1 
Thanks for pointing that out. Is the method correct ?

August 2nd, 2017, 07:19 AM  #6 
Senior Member Joined: May 2016 From: USA Posts: 743 Thanks: 301  I think you misunderstand the purpose behind factoring. (Factorizing is just a silly word.) The purpose is to get an expression into an equivalent expression that is more convenient for some purpose. There may be quite a few equivalent expressions. Which one is "correct" depends on what you want to do. So your expression for d would have been equivalent and would be therefore A "correct" answer if you had not made that sign error. In other words, your method is valid but not uniquely valid. I suspect that they want a different "correct" answer, namely an answer based on the method of difference of squares. $16a^2 = (4a)^2. \text{ And obviously } (3b + 4c)^2 \text{ is a square.}$ So $16a^2  (3b + 4c)^2 = \{4a  (3b + 4c)\}\{4a + (3b + 4c)\} =$ $(4a  3b  4c)(4a + 3b + 4c).$ Last edited by skipjack; August 4th, 2017 at 02:15 AM. 
August 2nd, 2017, 07:47 AM  #7  
Math Team Joined: Jul 2011 From: Texas Posts: 2,598 Thanks: 1287  Quote:
$3a(xy3) + b(xy3)$ $(xy3)(3a+b)$  
August 2nd, 2017, 08:04 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 17,719 Thanks: 1359 
(a) 6x²  21xy + 8xz  28yz = 3x(2x  7y) + 4z(2x  7y). That leads to (3x + 4z)(2x  7y). (c) Correct. (b) Use the difference of squares method (as per (c)). (e) 3ax + bx  3ay  by  9a  3b = (3a + b)x  (3a + b)y  3(3a + b) = (x  y  3)(3a + b) In hindsight, it can be seen that all the questions have been designed to be easy. It's a good idea to be well aware of the easiest methods and how to see whether they are immediately applicable. 

Tags 
checking or show, method 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Checking Mistake.  jiasyuen  Calculus  3  January 30th, 2015 05:16 PM 
Checking if f(x,y) is one to one.  marble1112  Applied Math  5  April 29th, 2012 09:28 PM 
checking continuity  Sambit  Real Analysis  32  December 4th, 2010 04:26 AM 
Show with Simplex Method  coolhandluke  Linear Algebra  0  September 21st, 2010 11:16 AM 
just checking  paulwall  Algebra  3  February 4th, 2009 10:34 AM 