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

1 Answer
MathFact-orials.blogspot.com
May 24, 2017

-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

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