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Given:
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\n" ); document.write( "(5x - 6)(5x - 6)
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\n" ); document.write( "The given operation is multiplication and you have two quantities to multiply. Each quantity
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\n" ); document.write( "This problem is of the form (a + b)(c + d) and you can do it by taking the first term in the
\n" ); document.write( "set of parentheses and using it to multiply each of the two terms in the second set of
\n" ); document.write( "parentheses. Then take the second term in the first set and use it to multiply each term
\n" ); document.write( "in the second set of parentheses. Finally you collect all the products and combine them as
\n" ); document.write( "rules permit. So using this process, you would first take \"a\" and use it to multiply
\n" ); document.write( "(c + d). The result would be a*c + a*d. Then you would take the second term, \"b\", and use it
\n" ); document.write( "to multiply (c + d). The result would be b*c + b*d. So you would have four answers to
\n" ); document.write( "combine ... ac + ad + bc + bd.
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\n" ); document.write( "Once you get familiar with this process the pattern will come to you naturally, and the
\n" ); document.write( "pattern will make sense.
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\n" ); document.write( "Now let's return to the problem you were given and apply this pattern to it:
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\n" ); document.write( "(5x - 6)(5x - 6)
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\n" ); document.write( "From the first (left hand) set of parentheses take the 5x and use it to multiply both terms
\n" ); document.write( "in the second set of parentheses. The products are (5x)*(5x) and (5x)(-6) and the two
\n" ); document.write( "results are 25x^2 and -30x.
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\n" ); document.write( "Next, from the first (left hand) set of parentheses take the -6 and use it to multiply both
\n" ); document.write( "terms in the second set of parentheses. The products are (-6)*(5x) and (-6)*(-6) and the
\n" ); document.write( "two results are -30x and + 36.
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\n" ); document.write( "So all four products are 25x^2 - 30x - 30x + 36. Notice that the two -30x terms can be added
\n" ); document.write( "together to get -60x. Therefore, the final answer is:
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\n" ); document.write( "Hope this helps you to understand the process and a pattern you can use to multiply
\n" ); document.write( "two binomials.
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\n" ); document.write( "You can use the same general procedure to multiply a binomial times a trinomial, two trinomials,
\n" ); document.write( "and so forth.
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\n" ); document.write( "For example ... to multiply (a + b)*(c + d + e) which is multiplying a binomial times a trinomial
\n" ); document.write( "you just take (one at a time) the two terms in the binomial and multiply them times each
\n" ); document.write( "term in the trinomial. So the products you would get are a*c, then a*d, then a*e. Once
\n" ); document.write( "you are that far, you take the second term of the binomial and multiply it times each of the
\n" ); document.write( "three terms in the trinomial to get b*c, then b*d, then b*e. You then have 6 products as
\n" ); document.write( "follows: a*c + a*d + a*e + b*c + b*d + b*e
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\n" ); document.write( "All you have to do then is to see if any of the products can be combined with other products.
\n" ); document.write( "Do all the possible combinations and the resulting terms are the answer.
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\n" ); document.write( "In shortened form ... multiply (a + b + c) times (d + e + f) ...
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\n" ); document.write( "The products are a*d + a*e + a*f + b*d + b*e + b*f + c*d + c*e +c*f
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\n" ); document.write( "Then all you do is look at these 9 answers and combine all the like terms you can find to
\n" ); document.write( "get the final answer. This may give you a better feel for how the pattern works and the
\n" ); document.write( "process of taking the terms in the first set of parentheses one at a time and using them to
\n" ); document.write( "multiply each of the terms in the second set of parentheses to come up with the answer. \n" ); document.write( "