What is the standard form of #y= (x-3)(4-x)+3x-2#?

1 Answer

#-x^2+10x-14#

Explanation:

Let's first do the multiplication of the brackets using FOIL, then add in the remaining terms:

FOIL

  • #color(red)(F)# - First terms - #(color(red)(a)+b)(color(red)(c)+d)#
  • #color(brown)(O)# - Outside terms - #(color(brown)(a)+b)(c+color(brown)d)#
  • #color(blue)(I)# - Inside terms - #(a+color(blue)b)(color(blue)(c)+d)#
  • #color(green)(L)# - Last terms - #(a+color(green)b)(c+color(green)d)#

and so #(x-3)(4-x)# becomes:

  • #color(red)(F) = 4x#
  • #color(brown)(O)=-x^2#
  • #color(blue)(I)=-12#
  • #color(green)(L)=3x#

which adds to:

#4x-x^2-12+3x=-x^2+7x-12#

Now let's add in the remaining terms:

#(-x^2+7x-12)+3x-2=-x^2+10x-14#