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

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Answer 1 · 2017-02-26T19:44:15

See the entire solution process below:

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:

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

$n^2 + 10n + 25$

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