# Expanding Brackets and Collecting Like Terms

## Expanding Brackets and Collecting Like Terms

# Expanding Brackets

- When you see an expression in the form of
**a(b + c)**, it means to distribute the ‘a’ to each term inside the brackets. This is known as expanding the brackets. - For example, if you have 3(x + 2), you multiply 3 by both ‘x’ and ‘2’ to get
**3x + 6**. - If you have brackets inside brackets, as in a nested expression like (a + (b + c)), deal with the innermost brackets first before expanding outer brackets.
- This process is governed by the
**distributive law**, which states that multiplication distributes over addition.

# Collecting Like Terms

- “Like terms” refers to terms that have exactly the same variable(s) and power(s). For example,
**3x²**and**5x²**are like terms. - To simplify an expression, you can gather like terms together and add or subtract their numerical coefficients. This process is known as
**collecting like terms**. - For example, in the expression 5x - 2x² + 3x + x², you can collect the like terms to get (5x+3x) + (-2x²+x²) which simplifies to
**8x - x²**. - The
**commutative property**(a + b = b + a) and**associative property**((a + b) + c = a + (b + c)) of addition allow us to rearrange and group terms as we wish when collecting like terms.

By practising these processes, you should become confident in handling any problems involving **expanding brackets** and **collecting like terms**.