Question

What is the standard form of `y= (12x+3)(7x-5)`?

Answer 1

`y = 84x^2 - 39x - 15`

Explanation:

To put this equation in standard form you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`y = (color(red)(12x) + color(red)(3))(color(blue)(7x) - color(blue)(5))` becomes:

`y = (color(red)(12x) xx color(blue)(7x)) - (color(red)(12x) xx color(blue)(5)) + (color(red)(3) xx color(blue)(7x)) - (color(red)(3) xx color(blue)(5))`

`y = 84x^2 - 60x + 21x - 15`

We can now combine like terms:

`y = 84x^2 + (-60 + 21)x - 15`

`y = 84x^2 - 39x - 15`