Question

How do you find the product of `(7x^2 + 5y + 7) (y + 5)`?

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)(7x^2) + color(red)(5y) + color(red)(7))(color(blue)(y) + color(blue)(5))` becomes:

`(color(red)(7x^2) xx color(blue)(y)) + (color(red)(7x^2) xx color(blue)(5)) + (color(red)(5y) xx color(blue)(y)) + (color(red)(5y) xx color(blue)(5)) + (color(red)(7) xx color(blue)(y)) + (color(red)(7) xx color(blue)(5))`

`7x^2y + 35x^2 + 5y^2 + 25y + 7y + 35`

We can now combine like terms:

`7x^2y + 35x^2 + 5y^2 + (25 + 7)y + 35`

`7x^2y + 35x^2 + 5y^2 + 32y + 35`