Which expression is a factored form of x^2 - 9? A) (x - 3)^2 {(x −…

Step by step

The question

Question: factor x² − 9.

Factor means: write it as a times, with brackets.

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Two squares

This is one square take away another square.

x times x is x².

3 times 3 is 9.

The rule: one bracket with plus, one with minus.

When we multiply them back, the middle parts cancel.

So we get (x + 3)(x − 3).

2 Check

Let's check: we multiply it back out.

Each part of the first bracket times each part of the second.

We get x² − 9 again.

So (x + 3)(x − 3) is right!

3 Pick the choice

Our answer is (x + 3)(x − 3).

That is choice B.

4 Why not the others

A is (x − 3)².

Wrong: (x − 3)² is x² − 6x + 9.

C is (x − 9)(x + 1).

Wrong: that gives x² − 8x − 9.

D is (x + 3)².

Wrong: (x + 3)² is x² + 6x + 9.

Let's look back.

First: two squares.

Then: check.

Then: pick the choice.

Last: why not the others.