document.write( "Question 610655: Find the product: (2x-7y)(2x+7y) \n" ); document.write( "

Algebra.Com's Answer #384501 by ashipm01(26) $\"\"$ $\"About$

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To multiply those two polynomials, multiply each term in each polynomial by every term in every other polynomial. For this case, there are two polynomials and each of them has two terms, so the resulting expression will have four terms before simplification (2 polynomials * 2 terms / polynomial = 4 terms).\r
\n" ); document.write( "\n" ); document.write( "The original expression was
\n" ); document.write( " $\"+%282x-7y%29%2A%282x%2B7y%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "The first polynomial has the following two terms: $\"+2x+\"$ and $\"+-7y+\"$ \r
\n" ); document.write( "\n" ); document.write( "And the second polynomial has the following two terms: $\"+2x+\"$ and $\"+7y+\"$ \r
\n" ); document.write( "\n" ); document.write( "So you just need to multiply each term in the first polynomial by each term in the second polynomial and then sum the products. This results in the following term products:
\n" ); document.write( " $\"+2x+%2A+2x+\"$ , $\"+2x+%2A+7y+\"$ , $\"+-7y+%2A+2x+\"$ , and $\"+-7y+%2A+7y+\"$ \r
\n" ); document.write( "\n" ); document.write( "Performing the multiplications in each of the terms yields the following terms:
\n" ); document.write( " $\"+4x%5E2+\"$ , $\"+14xy+\"$ , $\"+-14xy+\"$ , and $\"+-49y%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( "Summing those terms results in the following expression:
\n" ); document.write( " $\"+4x%5E2+%2B+14xy+%2B+-14xy+%2B+-49y%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( "Which simplifies to the answer:
\n" ); document.write( " $\"+%282x-7y%29%2A%282x%2B7y%29+=+4x%5E2+-+49y%5E2+\"$ \n" ); document.write( "

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