Question 153362
Hi, Hope I can help,
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Can you please help me expand this set of numbers?
(3x-5)(2x+7)
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To expand these numbers we will use a method called the FOIL method ( First, Inner, Outer, Last)
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This is how, you multiply the numbers, and add them together
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{{{ (highlight (3x)-5)*( highlight (2x)+7) = F }}}
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{{{ (highlight (3x)-5)*(  2x + highlight (7)) = O }}}
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{{{ ( 3x - highlight (5))*( highlight (2x) +  7) = I }}}
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{{{ ( 3x - highlight (5))*(  2x + highlight (7)) = L }}}
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Remember that it is a negative 5, not positive( a minus sign in front of a number/variable means it is a negative number), and there is a positive 7( a plus sign, means it is a positive number)
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Multiply the highlighted numbers in each equation
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{{{ (3x)(2x) = 6x^2 = F }}}
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{{{ (3x)(7) = 21x = O }}}
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{{{ (-5)(2x) = -10x = I }}} ( Since it is a (-5))
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{{{ (-5)(7) = -35 = L }}} ( Since it is a (-5))
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We can now add our four answers together
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{{{ 6x^2 + 21x + (-10x) + (-35) }}}
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We can add/subtract like terms( we will add the "x's" together)
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It will become
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{{{ 6x^2 + 11x + (-35) }}} = {{{ 6x^2 + 11x - 35 }}}
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{{{ 6x^2 + 11x - 35 }}} is your answer, Remember (FOIL)(First, Inner, Outer, Last)
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{{{ (highlight (3x)-5)*( highlight (2x)+7) = F }}}
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{{{ (highlight (3x)-5)*(  2x + highlight (7)) = O }}}
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{{{ ( 3x - highlight (5))*( highlight (2x) +  7) = I }}}
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{{{ ( 3x - highlight (5))*(  2x + highlight (7)) = L }}}
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{{{ 6x^2 + 11x - 35 }}} is your answer
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Hope I helped, Levi