Step by step
The question
Question: simplify 6y − 3(y + 2).
Simplify means: write it shorter, with the same value.
6y − 3(y + 2)
1 Open the brackets
The (−3) in front of the bracket multiplies every part inside.
a(b + c) = ab + ac
So we write (−3) times each part.
= 6y + (−3)(y) + (−3)(2)
− × + = −
Watch the signs.
(−3) times y is −3y.
(−3) times 2 is −6.
= 6y − 3y − 6
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the y terms go together.
Each colour is one kind.
like terms = same letters,
same powers
6y − 3y is 3y.
It is like 6 apples take away 3 apples: that is 3 apples.
6y − 3y = 3y
So the expression is 3y − 6.
= 3y − 6
3 Check
Let's check.
We pick a number for each letter: y = 3.
We put it into the start.
Start: 6 × 3 − 3 × (3 + 2) = 18 − 3 × 5
= 18 − 15 = 3
Now into our answer.
Answer: 3 × 3 − 6 = 9 − 6 = 3
Both give 3.
Same value, so 3y − 6 is right!
Both give 3
Let's look back.
First: open the brackets.
Then: group like terms.
Last: check.
Answer
= 3y − 6