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#