 My Math Forum Factorizing 16x^4-81y^4, why is the answer written like this?

 Algebra Pre-Algebra and Basic Algebra Math Forum

 August 9th, 2015, 12:38 PM #1 Newbie   Joined: Aug 2015 From: UK Posts: 9 Thanks: 0 Factorizing 16x^4-81y^4, why is the answer written like this? I can understand how the answer is reached: square root both sides to make it (4x^2 + 9y^2) (4x^2 - 9y^2) Then factorize the latter brackets to get a final answer of (4x^2 + 9y^2) (2x + 3y) (2x - 3y) Is the reason for not factorizing further with the first set of brackets because the answer would be the same for both brackets as (2x + 3y) (2x + 3y) or (2x - 3y) (2x - 3y)? Why is this done? I want to be extra sure about the rules on this. August 9th, 2015, 02:11 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1676 $4x^2+9y^2$ is not factorable over the real numbers August 9th, 2015, 09:40 PM   #3
Global Moderator

Joined: Dec 2006

Posts: 21,107
Thanks: 2324

Quote:
 Originally Posted by Dalekcaan1963 I can understand how the answer is reached: square root both sides
Incorrect. Instead, use A² - B² ≡ (A - B)(A + B). August 10th, 2015, 11:00 AM   #4
Senior Member

Joined: Feb 2010

Posts: 714
Thanks: 151

Quote:
 Originally Posted by Dalekcaan1963 I can understand how the answer is reached: square root both sides to make it . . .
This shows an incomplete understanding of basic principles. If I said find the sum $\displaystyle 64+49$ would you "square root both sides" to get $\displaystyle 8+7$ and say the answer to $\displaystyle 64+49$ is 15?

You can perform the same operation to both sides of a relation ($\displaystyle =,<,$ etc.)

As has been pointed out, what you want in this problem is to apply the well-known factor pattern called difference of squares $\displaystyle x^2-y^2=(x+y)(x-y)$ Tags 16x481y4, answer, factorizing, written Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jiasyuen Algebra 10 January 23rd, 2015 02:09 PM jiasyuen Algebra 3 December 31st, 2014 10:06 PM gelatine1 Number Theory 4 August 27th, 2013 09:49 PM r-soy Physics 0 March 1st, 2012 08:06 AM apohz Algebra 3 April 15th, 2009 09:43 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      