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.

“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.