Question

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

Answer 1

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`