Expanding in Numbers
There are two ways to calculate 4(5 + 6)
This second method is called the distributive property and can also be used in algebra.
Expanding in Algebra
The expression 2(p + 3) means:
Therefore, if the brackets are removed then the result will be 2 lots of p and 2 lots of 3
Thus 2(p + 3) = 2 × p + 2 × 3 = 2p + 6
Removing brackets from an expression is known as expanding the expression.
This usually occurs when a term outside a bracket is multiplied by every term inside the bracket.
The outside term "distributes" itself over the inside terms. Thus the name the distributive property.
Distributive Property in Action
When an expression is expanded, each term inside the bracket is multiplied by the term outside the bracket.
When brackets have been expanded, the expression must be simplified further if possible.
Note When expanding a bracket with a NEGATIVE number in front, the signs of each term inside the bracket change.
Factorising an algebraic expression is the opposite process of expanding brackets.
A common factor is a number or letter that divides into each term of an expression.
If every term of the expression has a common factor, this common factor should be taken out and placed in front of a set of brackets.