How do you write in standard form y = 4(x + 5) - 2(x + 1)(x + 1)?

1 Answer
Jacobi J.
Jun 24, 2018

-2x^2+18

Explanation:

Since this expression has many parts, I will color-code it and tackle it one by one.

color(purple)(4(x+5))-2color(steelblue)((x+1)(x+1)

For the expression in purple, all we need to do is distribute the 4 to both terms in the parenthesis. Doing this, we now have

color(purple)(4x+20)-2color(steelblue)((x+1)(x+1))

What I have in blue, we can multiply with the mnemonic FOIL, which stands for Firsts, Outsides, Insides, Lasts. This is the order we multiply the terms in.

Foiling (x+1)(x+1):

  • First terms: x*x=x^2
  • Outside terms: x*1=x
  • Inside terms: 1*x=x
  • Last terms: 1*1=1

This simplifies to color(steelblue)(x^2+2x+1). We now have

color(purple)(4x+20)-2(color(steelblue)(x^2+2x+1))

Distributing the -2 to the blue terms gives us

color(purple)(4x+20)-color(steelblue)(2x^2-4x-2)

Combining like terms gives us

-2x^2+18

We see that our polynomial is in standard form, ax^2+bx+c. Notice that the x terms cancel out, so we don't have a bx term.

Hope this helps!

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