Question

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

Answer 1

`-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`