Question

What is the standard form of `y=(-x - 1) (x - 3)`?

Answer 1

`y = -x^2 + 2x + 3`

Explanation:

To convert this to standard form we need to multiply the two sets of terms in parenthesis. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`y = (color(red)(-x) - color(red)(1))(color(blue)(x) - color(blue)(3))` becomes:

`y = (color(red)(-x) xx color(blue)(x)) + (color(red)(-x) xx color(blue)(-3)) - (color(red)(1) xx color(blue)(x)) + (color(red)(1) xx color(blue)(3))`

`y = -x^2 + 3x - 1x + 3`

We can now combine like terms:

`y = -x^2 + (3 - 1)x + 3`

`y = -x^2 + 2x + 3`