<p>(x^2+a^2)(x^3+3b^3+1)-(x^2+a^2)(2b^3+1)</p>
<p>Can somebody please factor this for me and show me the reason for each step.</p>
<p>the answer is: (x^2+a^2)(x+b)(x^2-bx+b^2)</p>
<p>but I never quite get that.</p>
<p>Thanks a ton guys.</p>
<p>Okay, don’t kill me if I get this wrong:</p>
<p>(x^2+a^2)(x^3+3b^3+1)-(x^2+a^2)(2b^3+1)
The two terms have (x^2+a^2) in common, so you can think of this bracket as “X”, so it would be (x^3+3b^3+1)X - (2b^3+1)X. You would just leave the “X” part as is and subtract. It would become (x^3+b^3)(x^2+a^2)?</p>
<p>haha I’m probably wrong… someone else help</p>
<p>I get the exact same… but the answer in the book disagrees =/</p>
<p>Huh. In that case, I can’t help you. Sorry. Maybe the book is wrong? Check near the front of the book b/c sometimes, the publisher makes mistakes in the answer section and will include a page of new, updated answers. If there is no such sheet in your book, then the answer must be right and we’re both wrong lol</p>
<p>finally figured out the answer.</p>
<p>we both got:</p>
<p>(x^3+b^3)(x^2+a^2)</p>
<p>but we can further factor the first part to get</p>
<p>(x^2+a^2)(x+3)(x^2+xb+a^2)</p>