SOLUTION: (4x+y)(2x squared-xy+5y squared) find the product

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Question 74016: (4x+y)(2x squared-xy+5y squared) find the product
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
%284x%2By%29%2A%282x%5E2-xy+%2B5y%5E2%29
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Here's the general plan to find the product. Use each term in the first set of parentheses
one at a time and multiply it times each of the three terms in the second set of parentheses.
Then add all the resulting terms from both multiplications. Finally look for common terms
and combine them.
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Following that plan, let's multiply 4x times every term in the second set of parentheses.
(Remember that you will add exponents if the term from the second set of parentheses
already has an x in it.)
.

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Next multiply the three terms in the second set of parentheses by the +y from the first
set of parentheses to get:
.

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Add the results of the two multiplications together to get:
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8x%5E3+-4x%5E2y+%2B+20xy%5E2+%2B+2x%5E2y+-+xy%5E2+%2B5y%5E3
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Now look for common terms that can be combined:
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How about -4x%5E2y+ and 2x%5E2y. These add together to -2x%5E2y. When you
replace these two terms with the single resulting term the answer reduces to:
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8x%5E3+-2x%5E2y+%2B+20xy%5E2+-+xy%5E2+%2B5y%5E3
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Next, notice the two terms that contain xy%5E2. Combining these results in:
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20xy%5E2+-+xy%5E2+=+19xy%5E2
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and substituting this into the answer gives:
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8x%5E3+-2x%5E2y+%2B+19xy%5E2+%2B5y%5E3
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That's it. There are no more common terms so this is the answer to your multiplication
problem.
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Hope that you can track this.