Question

What is the standard form of `y= (4x-4x^2)(3x-8) -(2x+3)^2`?

Answer 1

`y=-12x^3+40x^2-40x-9`

Explanation:

The steps will be 'expand and collect like terms'. As part of that we will use the 'FOIL' procedure.

`y=(4x−4x^2)(3x−8)−(2x+3)^2`

`y=(4x−4x^2)(3x−8)−(2x+3)(2x+3)`

When we have two parentheses, each with 2 things in them, we use 'FOIL': firsts, outers, inners, lasts. That is, multiply the first thing in the first bracket by the first thing in the second, then multiply the 'outer' things, then the 'inner', then the 'last' things in each bracket.

`y=(12x^2-32x-12x^3+32x^2)−(4x^2+6x+6x+9)`

In removing the brackets, not the '`-`' sign in front of the second parenthesis.

`y=12x^2-32x-12x^3+32x^2−4x^2-6x-6x-9`

Now we collect like terms:

`y=-12x^3+40x^2-40x-9`