Question

How do you simplify the expression `(3m + n)(3m - n)`?

Answer 1

See the entire solution process below:

Explanation:

The product of this expression can be found using the rule:

`(a + b)(a - b) = a^2 - b^2`

Substituting `3m` for `a` and `n` for `b` gives:

`(3m + n)(3m - n) = (3m)^2 - n^2`

`(3m + n)(3m - n) = 9m^2 - n^2`

We can also multiply this out the long way. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(3m) + color(red)(n))(color(blue)(3m) - color(blue)(n))` becomes:

`(color(red)(3m) xx color(blue)(3m)) - (color(red)(3m) xx color(blue)(n)) + (color(red)(n) xx color(blue)(3m)) - (color(red)(n) xx color(blue)(n))`

`9m^2 - 3mn + 3mn - n^2`

`9m^2 - 0 - n^2`

`9m^2 - n^2`