<p>I was just reviewing problems from my Alg. 2 textbook and I had trouble with some factoring problems:</p>
<p>
[quote]
INSTRUCTIONS: For Problems 63 through 66, factor first by grouping terms 3 and 1 or 1 and 3, whichever gives a difference of two squares.</p>
<p>63. x^2 + 6x + 9 - y^2</p>
<p>64. x^2 - 10x + 25 + y^2</p>
<p>65. a^2 - b^2 + 2b - 1</p>
<p>66. x^2 - 4y^2 + 4y - 1
[/quote]
</p>
<p>How do you go about doing these? I don't understand the instructions. </p>
<p>Take problem 63 for instance:
Grouping terms:
(x^2 + 9) + 6x - y^2
How is do terms 1 and 3 form a difference of squares? I'm confused...</p>
<p>Thanks</p>
<p>First of all, you will never see anything remotely like this on the SAT.</p>
<p>Second, these are very strange questions. At best it is unclear what they want. Grouping terms 3 and 1 is the same as grouping terms 1 and 3, so the question must be written incorrectly.</p>
<p>x^2 + 9 is not factorable in the reals - it is the sum of 2 squares, not the difference of 2 squares.</p>
<p>If you are allowed to factor over the complexes, then x^2 + 9 = (x-3i)(x+3i). But I don’t see how this would help you to factor the expression given in problem 63.</p>
<p>I’m guessing what they want is:</p>
<p>x^2 + 6x + 9 - y^2 = (x+3)^2 - y^2 = (x+3-y)(x+3+y)</p>