Question

What is the standard form of `y= (3x-5)(2x+12)-7x^2+15x`?

Answer 1

See a solution process below:

Explanation:

First, multiply the two terms in parenthesis by multiplying each individual term in the left parenthesis by each individual term in the right parenthesis.

`y = (color(red)(3x) - color(red)(5))(color(blue)(2x) + color(blue)(12)) - 7x^2 + 15x` becomes:

`y = (color(red)(3x) xx color(blue)(2x)) + (color(red)(3x) xx color(blue)(12)) - (color(red)(5) xx color(blue)(2x)) - (color(red)(5) xx color(blue)(12)) - 7x^2 + 15x`

`y = 6x^2 + 36x - 10x - 60 - 7x^2 + 15x`

We can now group and combine like terms:

`y = 6x^2 - 7x^2 + 36x - 10x + 15x - 60`

`y = (6 - 7)x^2 + (36 - 10 + 15)x - 60`

`y = -1x^2 + 41x - 60`

`y = -x^2 + 41x - 60`