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:

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

$a^2 -18a + 81$

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