<PRE><B>Question 1199318</B>
Factor: 
(2m - 3)² - (8m² - 4)²

Notice: This question on my homework has a bonus mark. I&#39;m not sure why, and what&#39;s so special about it. Can someone help me find some extra &quot;bonus&quot; step at the end?

Thanks! 
&lt;pre&gt;This is a DOTS (Difference of Two Squares) factorization.

(2m - 3)² - (8m² - 4)²
[(2m - 3) - (8m&lt;sup&gt;2&lt;/sup&gt; - 4)][(2m - 3) + (8m&lt;sup&gt;2&lt;/sup&gt; - 4)] ------ Applying DOTS, or {{{matrix(1,3, a^2 - b^2, &quot;=&quot;, (a - b)(a + b))}}}
(2m - 3 - 8m&lt;sup&gt;2&lt;/sup&gt; + 4)(2m - 3 + 8m&lt;sup&gt;2&lt;/sup&gt; - 4)
(- 8m&lt;sup&gt;2&lt;/sup&gt; + 2m + 1)(8m&lt;sup&gt;2&lt;/sup&gt; + 2m - 7)
(- 8m&lt;sup&gt;2&lt;/sup&gt; + 4m - 2m + 1)(8m&lt;sup&gt;2&lt;/sup&gt; + 2m - 7) ----- Factoring - 8m&lt;sup&gt;2&lt;/sup&gt; + 2m + 1
(&lt;u&gt;- 8m&lt;sup&gt;2&lt;/sup&gt; + 4m&lt;/u&gt; - &lt;u&gt;2m + 1&lt;/u&gt;)(8m&lt;sup&gt;2&lt;/sup&gt; + 2m - 7)
[- 4m(2m - 1) - 1(2m - 1)](8m&lt;sup&gt;2&lt;/sup&gt; + 2m - 7)
&lt;font color = blue&gt;&lt;font size  = 4&gt;&lt;b&gt;(- 4m - 1)(2m - 1)(8m&lt;sup&gt;2&lt;/sup&gt; + 2m - 7)      or     - (4m + 1)(2m - 1)(8m&lt;sup&gt;2&lt;/sup&gt; + 2m - 7)&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/pre&gt;</PRE>