How do i factor this36(2x-y)^2-25(u-2y)^2

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Discussion Overview

The discussion revolves around the factoring of the expression 36(2x-y)² - 25(u-2y)². Participants explore methods for factoring, particularly focusing on the difference of squares and the implications of coefficients outside the brackets.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant suggests expanding the brackets first but expresses uncertainty about this approach.
  • Another participant notes that the expression represents a difference of two squares, which can be factored using the formula a² - b² = (a + b)(a - b).
  • A participant questions how to handle the coefficients 25 and 36 that are outside the brackets after applying the difference of squares method.
  • It is pointed out that after factoring, the coefficients 25 and 36 will not remain outside the brackets.
  • One participant identifies that 5² equals 25 and 6² equals 36, indicating a potential simplification.
  • A participant proposes substituting variables (let 2x - y = A and u - 2y = B) to rewrite the expression as 36(A²) - 25(B²) = (6A)² - (5B)².
  • Another participant suggests that rewriting 36(2x-y)² as (6(2x-y))² may simplify the factoring process for the second term as well.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to factor the expression, and multiple methods and viewpoints are presented without resolution.

Contextual Notes

The discussion includes various assumptions about the steps involved in factoring and the handling of coefficients, which remain unresolved.

dcgirl16
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how do i factor this
36(2x-y)^2-25(u-2y)^2

i was thinking to expand the brackets first?? but I am not really sure
 
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In general the difference of two squares (which is what you have) is easily factored.

a^2-b^2=(a+b)(a-b)
 
alright so once I've got that what do i do with the 25 and 36 outside the brackets
 
Once you 'do that' you don't have any 25 or 36 outside any brackets.
 
5^2 = 25
6^2 = 36
 
Let 2x-y=A and u=2y=B

36(A^2) - 25(B^2)= (6A)^2 - (5B)^2
 
Since we know 6^2 = 36 could you do it easier if it was written as: 36(2x-y)^2 = 6^2(2x-y)^2 = [(6)(2x-y)]^2 and you did the same process to simplify the other term.
 

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