Question

How do you multiply `(n+5)^2`?

Answer 1

See the entire solution process below:

Explanation:

Solution 1) You can use the formula: `(a + b)^2 = a^2 + 2ab + b^2`

Substituting `n` for `a` and `5` for `b` gives:

`(n + 5)^2 = n^2 + 2(n5) + 5^2 = n^2 + 10n + 25`

Solution 2) To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(n) + color(red)(5))(color(blue)(n) + color(blue)(5))` becomes:

`(color(red)(n) xx color(blue)(n)) + (color(red)(n) xx color(blue)(5)) + (color(red)(5) xx color(blue)(n)) + (color(red)(5) xx color(blue)(5))`

`n^2 + 5n + 5n + 25`

We can now combine like terms:

`n^2 + (5 + 5)n + 25`

`n^2 + 10n + 25`