How do you simplify the product #(a - 6)(a + 8)# and write it in standard form?

1 Answer
Johnson Z.
Mar 3, 2016

#a^2+2a-48#

Explanation:

For simplifying a quadratic equation into standard form, the F.O.I.L. (first, outside, inside, last) method is often used to expand the brackets. Here is what you will need to know before we start:

http://math.tutorvista.com/algebra/foil-method.html

#1#. Use the F.O.I.L. (first, outside, inside, last) method to expand the brackets.

#(color(red)a# #color(blue)(-6))(color(orange)a# #color(green)(+8))#

#2#. For the "F" (first) in F.O.I.L., multiply the two #a#'s together.

#color(red)a(color(orange)a)#

#=color(purple)(a^2)#

#3#. For the "O" (outside) in F.O.I.L., multiply the first #color(red)a# and #color(green)8# together.

#color(purple)(a^2)# #color(red)(+a)(color(green)8)#

#=color(purple)(a^2)# #color(purple)(+8a)#

#4#. For the "I" (inside) in F.O.I.L., multiply #color(blue)(-6)# and the second #color(orange)a# together.

#color(purple)(a^2)# #color(purple)(+8a)# #color(blue)(-6)(color(orange)a)#

#=color(purple)(a^2)# #color(purple)(+8a)# #color(purple)(-6a)#

#5#. For the "L" (last) in F.O.I.L., multiply #color(blue)(-6)# and #color(green)(8)# together.

#color(purple)(a^2)# #color(purple)(+8a)# #color(purple)(-6a)# #color(blue)(-6)color(green)((8))#

#=color(purple)(a^2)# #color(purple)(+8a)# #color(purple)(-6a)# #color(purple)(-48)#

#6#. Recall that the general quadratic equation in standard form is: #ax^2+bx+c=0#. Thus, simplify the equation.

#=color(purple)(a^2+2a-48)#

#:.#, the equation in standard form is #a^2+2a-48#.

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