SOLUTION: Factor: (2m - 3)² - (8m² - 4)² Notice: This question on my homework has a bonus mark. I'm not sure why, and what's so special about it. Can someone help me find some extra

Algebra ->  Equations -> SOLUTION: Factor: (2m - 3)² - (8m² - 4)² Notice: This question on my homework has a bonus mark. I'm not sure why, and what's so special about it. Can someone help me find some extra       Log On


   

Question 1199318: Factor:
(2m - 3)² - (8m² - 4)²
Notice: This question on my homework has a bonus mark. I'm not sure why, and what's so special about it. Can someone help me find some extra "bonus" step at the end?
Thanks!
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%282m+-+3%29%5E2+-+%288m%5E2+-+4%29%5E2

=4m%5E2+-+12m+%2B+9+-+%2864m%5E4+-+64m%5E2+%2B+16%29
=4m%5E2+-+12m+%2B+9+-+64m%5E4+%2B+64m%5E2+-+16
=-64m%5E4+%2B+68m%5E2+-+12m+-+7
=-64m%5E4%2B16m%5E3%2B64m%5E2-28m-16m%5E3%2B4m%5E2%2B16m-7
=%28-64m%5E4-16m%5E3%29%2B%2816m%5E3%2B4m%5E2%29%2B%2864m%5E2%2B16m%29-%2828m%2B7%29
=-16m%5E3%284m%2B1%29%2B4m%5E2%284m%2B1%29%2B16m%284m%2B1%29-7%284m%2B1%29
=%284m%2B1%29%28-16m%5E3%2B4m%5E2%2B16m-7%29
=%284m%2B1%29%28-%2816m%5E3-4m%5E2-16m%2B7%29%29
=-%284m+%2B+1%29+%2816m%5E3+-+4m%5E2+-+16m+%2B+7%29
=-%284m+%2B+1%29+%2816m%5E3%2B+4m%5E2-14m-+8m%5E2+-+2m+%2B+7%29
=-%284m+%2B+1%29+%28%2816m%5E3%2B+4m%5E2-14m%29-+%288m%5E2+%2B+2m+-7%29%29
=-%284m+%2B+1%29+%282m%288m%5E2%2B+2m-7%29-+%288m%5E2+%2B+2m+-+7%29%29
=-%284m+%2B+1%29+%282m+-+1%29+%288m%5E2+%2B+2m+-+7%29


Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

There is nothing special in it :   it is a regular routine.


If you wish,  I can recommend you more interesting deal as a bonus :  read and solve logical problems from this lesson

    - Some logic problems

in this site.


/////////////////


I do not recommend you to solve the problem as @MathLover1 does.

There is much simpler method/way: use an identify a^2 - b^2 = (a-b)*(a+b).


You will easily complete the transformations, and you will NEVER and NOWHERE work with high-degree polynomials.

Your polynomials in parentheses will be quadratic, and you will complete the assignment to the end
without having any trouble.


This lady always chooses the most inappropriate way, the worst of all possible ways.


Why ? - Because she simply does not know the subject and is not able to teach properly.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
(2m - 3)² - (8m² - 4)²
Notice: This question on my homework has a bonus mark. I'm not sure why, and what's so special about it. Can someone help me find some extra "bonus" step at the end?
Thanks! 
This is a DOTS (Difference of Two Squares) factorization.

(2m - 3)² - (8m² - 4)²
[(2m - 3) - (8m2 - 4)][(2m - 3) + (8m2 - 4)] ------ Applying DOTS, or matrix%281%2C3%2C+a%5E2+-+b%5E2%2C+%22=%22%2C+%28a+-+b%29%28a+%2B+b%29%29
(2m - 3 - 8m2 + 4)(2m - 3 + 8m2 - 4)
(- 8m2 + 2m + 1)(8m2 + 2m - 7)
(- 8m2 + 4m - 2m + 1)(8m2 + 2m - 7) ----- Factoring - 8m2 + 2m + 1
(- 8m2 + 4m - 2m + 1)(8m2 + 2m - 7)
[- 4m(2m - 1) - 1(2m - 1)](8m2 + 2m - 7)
(- 4m - 1)(2m - 1)(8m2 + 2m - 7)      or     - (4m + 1)(2m - 1)(8m2 + 2m - 7)