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

1 Answer
Apr 11, 2017

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#