Are 4(n - 2) and 4n - 2 equivalent

Step by step

The question

Question: are 4(n − 2) and 4n − 2 equivalent?

Equivalent means: the two are equal, whatever number the letter is.

First we simplify the first one: 4(n − 2).

We write it shorter, with the same value.

1 Open the brackets

The 4 in front of the bracket multiplies every part inside.

So we write 4 times each part.

Watch the signs.

4 times n is 4n.

4 times (−2) is −8.

2 Compare

4n − 8 and 4n − 2 are not the same.

Careful!

The 4 multiplies both parts in the bracket, the 2 too.

So no: they are not equivalent.

3 Check

Let's check with a number: n = 2.

The first gives 0.

The second gives 6.

Different.

So the answer is right!

Let's look back.

First: open the brackets.

Then: compare.

Last: check.