<p>There are threads regarding this question on the consolidated list of math solutions page, but no one ever bothers to respond to those anymore.
Question 18 on BB page 657.</p>
<p>I understand the process of getting the answer, but i still have a few unanswered questions.</p>
<p>First we get to 6=c-d^2 , and then we get
106=c-(d-4(2.5))^2 with the values plugged in. From this step, almost everyone expanded the binomial
106=c-(d-10)^2 into
106=c - d2+20D-100</p>
<p>My questions are
1. Why do we have to expand it, is there something that tells us we should expand the binomial?
2. Why wouldn't not expanding it, and turning
106=c-(d-10)^2 into
106=c-d^2+100 work?! </p>
<p>3.When we foil it, it should be D^2-20D+100 . Turning it to D^2-20D+100(the correct form) would mean we apply the negative sign after foiling. Is that correct?</p>
<ol>
<li>I don’t have the book.</li>
<li>It doesn’t work because that’s not how you foil things.</li>
<li>D^2-20D+100 is correct, and since that’s being subtracted, you need to change all the signs.</li>
</ol>
<ol>
<li>You expand it because to solve the problem you’ll have to substitute 6 for c-d^2 in another equation.</li>
<li>That’s not how you FOIL.</li>
<li>Yes.</li>
</ol>
<ol>
<li>You usually expand the binomial so you can work with the other equation and then reduce them. Because the equation is</li>
</ol>
<p>106 = c - d2 + 20d - 100 we can move 100 to the other side to simplify then subtract from other equation.</p>
<ol>
<li><p>That won’t work because (a+b)^2 doesn’t equally a2 + b2</p></li>
<li><p>Yes, the negative sign flips all the signs around. - because +</p></li>
</ol>