Step by step
The question
Question: simplify 3x(x − 2).
Simplify means: write it shorter, with the same value.
3x(x − 2)
1 Open the brackets
The 3x in front of the bracket multiplies every part inside.
a(b + c) = ab + ac
So we write 3x times each part.
= 3x(x) + 3x(−2)
− × + = −
Watch the signs.
3x times x is 3x².
3x times (−2) is −6x.
= 3x2 − 6x
2 Check
Let's check.
We pick a number for each letter: x = 3.
We put it into the start.
Start: 3 × 3 × (3 − 2) = 9 × 1 = 9
Now into our answer.
Answer: 3 × 32 − 6 × 3 = 27 − 18 = 9
Both give 9.
Same value, so 3x² − 6x is right!
Both give 9
Let's look back.
First: open the brackets.
Last: check.
Answer
= 3x2 − 6x