document.write( "Question 984700: (x+6)(4x-3) \n" ); document.write( "

Algebra.Com's Answer #605491 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "You have two binomials (meaning two terms). Use FOIL, which stands for First, Outside, Inside, Last.
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document.write( "First:      x  and  4x   x times 4x is 4x²\r\n" );
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document.write( "Outside:    x  and  -3   x times -3 is -3x\r\n" );
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document.write( "Inside:     6  and  4x   6 times 4x is 24x\r\n" );
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document.write( "Last:       6  and  -3   6 times -3 is -18\r\n" );
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document.write( "Then add up the results:   4x² - 3x + 24x - 18\r\n" );
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document.write( "Almost done.  The two middle terms are \"like\" terms, so we can add them.  -3 + 24 is 21, so your final result is:\r\n" );
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document.write( "                           4x² + 21x -18\r\n" );
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\n" ); document.write( "Note that you don't have to do the multiplications in that exact order. You could do Last, Outside, First, Inside if you wanted to. But LOFI doesn't spell anything, so it is harder to remember than FOIL.\r
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\n" ); document.write( "\n" ); document.write( "Why This Works\r
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\n" ); document.write( "\n" ); document.write( "Remember the Distributive Property?\r
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\n" ); document.write( "\n" ); document.write( "for all real numbers, a, b, and c.\r
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\n" ); document.write( "\n" ); document.write( "Well what if

and

? Couldn't you substitute into the general form of the Distributive Property and get:\r
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\n" ); document.write( "\n" ); document.write( "And then, in the right hand side of the equation, distribute 4x across x + 6 and (-3) across x + 6 giving you the same result as the FOIL process?\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it\r
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