Expanding brackets in algebra

To expanding brackets means multiplying each term in the brackets by the expression outside the brackets.

Expanding brackets is the reverse process of factorisation and is sometimes referred to as multiplying out. In effect by expanding brackets you are removing the brackets.

To expand brackets we multiply everything outside of the bracket, by everything inside the bracket.

For a single bracket:

• Identify the term outside: the bracket and the terms inside.

• Multiply the outside term: by the first term inside.

• Multiply the outside term: by the second term inside.

• Combine the results: to form the expanded expression. 

For double brackets:

• Multiply the first term: in the first bracket by both terms in the second bracket. 

• Multiply the second term: in the first bracket by both terms in the second bracket. 

• Add and simplify: all the resulting terms. 

Factorising in Algebra

Factorising algebraic expressions involves rewriting them as a product of their factors, essentially reversing the process of expanding brackets. This is done by identifying the Highest Common Factor (HCF) of the terms, writing the HCF outside of a set of brackets, and then dividing each term in the original expression by the HCF to find the terms that go inside the brackets.  

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