How do you multiply #(a-9)^2#?

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Answer 1 · 2017-02-19T19:42:57

There are two ways to expand this. The first way is to use this rule:

#(x +- y)^2 = x^2 +- 2xy + y^2#

Substituting #a# for #x# and #9# for #b# from our problem gives:

#(a - 9)^2 = a^2 - 2a9 + 9^2 = a^2 - 18a + 81#

The second way is to first rewrite this expression as:

#(a - 9)(a - 9)#

Then, to multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(a) - color(red)(9))(color(blue)(a) - color(blue)(9))# becomes:

#(color(red)(a) xx color(blue)(a)) - (color(red)(a) xx color(blue)(9)) - (color(red)(9) xx color(blue)(a)) + (color(red)(9) xx color(blue)(9))#

#a^2 - 9a - 9a + 81#

We can now combine like terms:

#a^2 + (-9 - 9)a + 81#

#a^2 -18a + 81#