Question

How do you find the product `(3c+6d)^2`?

Answer 1

See the entire solution process below:

Explanation:

We can rewrite this expression as:

`(3x + 6d)(3x + 6d)`

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

`(color(red)(3c) + color(red)(6d))(color(blue)(3c) + color(blue)(6d))` becomes:

`(color(red)(3c) xx color(blue)(3c)) + (color(red)(3c) xx color(blue)(6d)) + (color(red)(6d) xx color(blue)(3c)) + (color(red)(6d) xx color(blue)(6d))`

`9c^2 + 18cd + 18cd + 36d^2`

We can now combine like terms:
`9c^2 + (18 + 18)cd + 36d^2`

`9c^2 + 36cd + 36d^2`