Grouping Symbols: Expanding Brackets

In short: Expanding brackets means multiplying the term outside by every term inside: $a(b+c)=ab+ac$. Keep each plus or minus sign, then collect any like terms.

Before you start

• No sign next to a bracket means multiply: $3(x+6)=3\times (x+6)$.
• Multiplying terms: $4\times 2x=8x$ and $x\times x=x^2$. (See Multiplying and Dividing Terms.)
• Collecting like terms: $3x+2x=5x$. (See Adding and Subtracting Terms.)

Brackets group things together

Brackets (also called grouping symbols) keep terms together as one package. The number or term outside multiplies the whole package.

Keep the plus or minus sign that was inside. In $5(5x-4)$, the 4 was being taken away, so $20$ is taken away too.

A letter outside

The rule is exactly the same when a letter is outside.

Expand, then collect

Often you expand two sets of brackets and then collect like terms.

Quick summary

• Brackets group terms. The term outside multiplies every term inside.
• $a(b+c)=ab+ac$.
• Keep the plus or minus sign from inside the brackets.
• A letter outside works the same way: $x(x+2)=x^2+2x$.
• After expanding, collect like terms.
• Check by putting in a small number such as 1.

Quiz