Lexa W.
asked • 02/09/17Where did the "a" come from in this answer and how come the final bit isn't negative?
I'm reading this book called "Get Math" and one part of the book says -b(a2+2ab+b2) = -a2b - 2ab2 +ab3. My first question is where did the "a"come from and my second one is how come the last bit isn't negative?
The original problem is (a+b)2 (a-b).
The original problem is (a+b)2 (a-b).
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1 Expert Answer
Kenneth S. answered • 02/09/17
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(a+b)2 (a-b) = (a-b)(a2 + 2ab + b2)
Can you now complete this job?
Lexa W.
(a-b)(a2 + 2ab +b2) = a3 + 2a2b + ab2 - a2b - 2ab2 -b3 ? That's what I think it should be.
In the book I'm reading (a+b)2 (a-b) becomes a(a2 + 2ab + b2) - b(a2 + 2ab + b2). I feel like I understand how the distributing of "a" works in the first part of the problem. It makes sense to me. What I do get is if I'm distributing a -b how is there an a in the answer and why is the bit not negative?
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02/09/17
Jonathan C.
-b(a2 + 2ab + b2) = -ba2 - 2ab2 - b3
If what you have at the top is what is in the book (and nothing else), then it is incorrect. I was thinking that this was a fragment of that step, but there are no other terms that combine with b3. So, no matter which way I look at this, it is simply incorrect.
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02/09/17
Lexa W.
So I'm right and my book is wrong? That's what I was thinking. I thought I was just missing something. The book I'm using isn't a conventional math book. One of the writers is supposed to be a mathematician though. Before this the rest of the material in the book turned out to be correct. Since it's not a conventional math book I've been checking to make sure everything being said is correct.
I wish I could attach a screenshot of the book. After stating -b(a2 +2ab + b2) = -a2b - 2ab2 +ab3. The author displays both expressions together a3 + 2a2b + ab2 - a2b - 2ab2 + ab3.
After that it says "Here, we have 2a²b and −a²b, which leaves us with a²b. We also have ab ² and −2ab², giving us −ab². The original expression will become the following:"
(a+b)2 (a-b) = a3 + a2b - ab2 - b3.
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02/09/17
Kenneth S.
Lexa's answer (a+b)2 (a-b) = a3 + a2b - ab2 - b3 is the CORRECT FINAL ANSWER.
If your book says anything else, it's wrong and you should report it to (a) your parents and (b) your teacher.
They should be teaching you long multiplication of polynomials.
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02/10/17
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Lexa W.
02/09/17