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

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

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Answer 1 · 2017-04-11T21:21:44

See the entire solution process below:

Explanation:

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

$(a + b) (a - b) = a^{2} - b^{2}$ $(a + b)(a - b) = a^2 - b^2$

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

$(3 m + n) (3 m - n) = {(3 m)}^{2} - n^{2}$ $(3m + n)(3m - n) = (3m)^2 - n^2$

$(3 m + n) (3 m - n) = 9 m^{2} - n^{2}$ $(3m + n)(3m - n) = 9m^2 - n^2$

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.

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

$(3 m \times 3 m) - (3 m \times n) + (n \times 3 m) - (n \times n)$ $(color(red)(3m) xx color(blue)(3m)) - (color(red)(3m) xx color(blue)(n)) + (color(red)(n) xx color(blue)(3m)) - (color(red)(n) xx color(blue)(n))$

$9 m^{2} - 3 m n + 3 m n - n^{2}$ $9m^2 - 3mn + 3mn - n^2$

$9 m^{2} - 0 - n^{2}$ $9m^2 - 0 - n^2$

$9 m^{2} - n^{2}$ $9m^2 - n^2$

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

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