document.write( "Question 578037: how do you expand this expression and I know that you use associative property but how do I use it in this sort of expression. please help I am very curious.
\n" ); document.write( "thanks\r
\n" ); document.write( "\n" ); document.write( "(3x-1)(2x+5) \n" ); document.write( "

Algebra.Com's Answer #370492 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
There is the practical procedure that everyone uses, and the theory behind it, that few remember or care about.
\n" ); document.write( "THE PRACTICAL PROCEDURE
\n" ); document.write( "Each factor is a sum of two terms.
\n" ); document.write( "In 3x-1, the first term is 3x and the last term is -1.
\n" ); document.write( "In 2x+5, the first term is 2x and the last term is 5.
\n" ); document.write( "It is accepted that we skip intermediate calculations that are part of the theory, and just write the end result, which is the sum of all 4 possible products of one term from each factor. To make sure all those 4 products are accounted for, we use the acronym or mnemonic FOIL. It stands for:
\n" ); document.write( "F _ First=product of first terms - $\"%283x%29%2A%282x%29=6x%5E2\"$
\n" ); document.write( "O _ Outside=product of terms written on the outside of the product - $\"%283x%29%2A5=15x\"$
\n" ); document.write( "I _ Inside=product of terms written on the inside of the product - $\"%28-1%29%2A%282x%29=-2x\"$
\n" ); document.write( "L _ Last=product of both last terms - $\"%28-1%29%2A5=-5\"$
\n" ); document.write( "So we write
\n" ); document.write( " $\"%283x-1%29%282x%2B5%29=6x%5E2%2B15x-2x-5\"$ without any more explanations, because when you get to a certain point in algebra you are allowed to skip the steps that you can do in your head, automatically.
\n" ); document.write( "Next we \"collect like terms\", meaning adding $\"15x-2x=13x\"$
\n" ); document.write( "So the whole solution would be written as
\n" ); document.write( " $\"%283x-1%29%282x%2B5%29=6x%5E2%2B15x-2x-5=6x%5E2%2B13x-5\"$
\n" ); document.write( "THE THEORY
\n" ); document.write( "The long theoretical explanation for \"FOIL\" is that you use the distributive property twice.
\n" ); document.write( "It goes like this:
\n" ); document.write( "

\n" ); document.write( "The distributive property is stated, in general terms as
\n" ); document.write( " $\"%28a%2Bb%29%2Ac=a%2Ac%2Bb%2Ac\"$ and we use it, without even thinking about it, each time we multiply a number with two or more digits:
\n" ); document.write( " $\"17%2A3=%2810%2B7%29%2A3=10%2A3%2B7%2A3=30%2B21=51\"$
\n" ); document.write( "Incidentally, in $\"15x-2x=13x\"$ you are also using the distributive property, apparently backwards:
\n" ); document.write( " $\"15x-2x=%2815-2%29x=13x\"$
\n" ); document.write( "The associative property is the one that says that if you have more that two numbers to multiply, you can multiply any pair first.
\n" ); document.write( "So we can calculate $\"81%2A5%2A2\"$ as $\"81%2A%285%2A2%29=81%2A10=810\"$ , which gives you the same result, but is much easier that having to multiply 81 times 5 first.
\n" ); document.write( "I hope you were really so very curious that you enjoyed the long explanation. \n" ); document.write( "

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