Question

How do you find the product `(2y-11)(y^2-3y+2)`?

Answer 1

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(2y) - color(red)(11))(color(blue)(y^2) - color(blue)(3y) + color(blue)(2))` becomes:

`(color(red)(2y) xx color(blue)(y^2)) - (color(red)(2y) xx color(blue)(3y)) + (color(red)(2y) xx color(blue)(2)) - (color(red)(11) xx color(blue)(y^2)) + (color(red)(11) xx color(blue)(3y)) - (color(red)(11) xx color(blue)(2))`

`2y^3 - 6y^2 + 4y - 11y^2 + 33y - 22`

We can now group and combine like terms:

`2y^3 - 6y^2 - 11y^2 + 4y + 33y - 22`

`2y^3 + (-6 - 11)y^2 + (4 + 33)y - 22`

`2y^3 + (-17)y^2 + 37y - 22`

`2y^3 - 17y^2 + 37y - 22`