Question

How do you multiply `(3a-7b)^2`?

Answer 1

See the entire multiplication process below:

Explanation:

This problem can be rewritten as:

`(color(red)(3a) - color(red)(7b))(color(blue)(3a) - color(blue)(7b))`

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

`(color(red)(3a) - color(red)(7b))(color(blue)(3a) - color(blue)(7b))` becomes:

`(color(red)(3a) xx color(blue)(3a)) - (color(red)(3a) xx color(blue)(7b)) - (color(red)(7b) xx color(blue)(3a)) + (color(red)(7b) xx color(blue)(7b))`

`9a^2 - 21ab - 21ab + 49b^2`

We can now combine like terms:

`9a^2 + (-21 - 21)ab + 49b^2`

`9a^2 - 42ab + 49b^2`