Question

How do you multiply `(2x+3v)^2`?

Answer 1

See the entire solution process below.

Explanation:

We can rewrite this express as:

`(2x + 3v)(2x + 3v)`

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

`(color(red)(2x) + color(red)(3v))(color(blue)(2x) + color(blue)(3v))` becomes:

`(color(red)(2x) xx color(blue)(2x)) + (color(red)(2x) xx color(blue)(3v)) + (color(red)(3v) xx color(blue)(2x)) + (color(red)(3v) xx color(blue)(3v))`

`4x^2 + 6xv + 6xv + 9v^2`

We can now combine like terms:

`4x^2 + (6 + 6)xv + 9v^2`

`4x^2 + 12xv + 9v^2`