Question

How do you put `y = (x - 2)(x - 7)` into standard form?

Answer 1

See a solution process below:

Explanation:

We can put this equation in standard form by multiplying the two terms on the right by multiplying each individual term in the left parenthesis by each individual term in the right parenthesis.

`y = (color(red)(x) - color(red)(2))(color(blue)(x) - color(blue)(7))` becomes:

`y = (color(red)(x) xx color(blue)(x)) - (color(red)(x) xx color(blue)(7)) - (color(red)(2) xx color(blue)(x)) + (color(red)(2) xx color(blue)(7))`

`y = x^2 - 7x - 2x + 14`

We can now combine like terms:

`y = x^2 + (-7 - 2)x + 14`

`y = x^2 + (-9)x + 14`

`y = x^2 - 9x + 14`