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ALGEBRA

EXPRESSIONS

Simplifying Algebra

An algebraic expression is simply a collection of terms. A term can be a number, a letter or a combination of the two. Expressions can be simplified, however we can only add and subtract when we have like terms. For example, if I have two apples and someone gives me three apples, I have five apples, and so I can say that 2a+3a is equal to 5a. If someone then gives me two bananas, I have five apples and two bananas (ie. 5a+2b). I cannot add these terms because they are not like terms.

Prior knowledge

  • Negative numbers

Key Terms

  • Expression: Collection of terms. 

  • Term: A number, letter or a combination of the two. 

  • Like terms: When two terms have the same variable raised to the same power.

  • Coefficient: The number that is multiplied by a letter. 

  • Variable: A value that can "vary", i.e. change. 

  • Polynomial: An expression with more than one term.

Forming Expressions

A key skill in maths is being able to form a mathematical expression from words. Once we know how to form expressions, we can use them to help us to solve equations and hence figure out unknown quantities. Using expressions can help us to problem solve. For example, if I have x sweets, and give three sweets to my sister, I now have x-3 sweets in total.

Prior knowledge

Key Terms

  • Expression: a collection of terms.

  • Forming an expression: Describing a sentence using numbers, letters and mathematical operations. 

Expanding Brackets

We often use brackets within expressions, however, sometimes it is useful to remove the brackets so that we can further simplify an expression. The process of putting brackets into an expression is called factorising, the process of removing the brackets is called expanding. Here, we will look at expanding brackets. 

Prior knowledge

Key Terms

  • Expanding brackets: Removing brackets from an expression

  • Simplifying: Collecting all of the like terms once the brackets have been removed. 

  • Single brackets: An expression with a single term outside one set of brackets, eg. x(x+2).

  • Double brackets: An expression with a pair of brackets next to each other, eg. (x+2)(x+3).

  • Triple brackets: An expression with three sets of brackets next to each other, eg. (x+1)(x+2)(x+3).

Factorising

Though it can be useful to expand brackets, it can sometimes be useful to put the brackets back in. This is a skill that comes in handy when solving equations, simplifying algebraic fractions and more. 

Prior knowledge

Key Terms

  • Factorising: Putting brackets into an expression i.e. splitting an expression into its "factors".

  • Factor: A term that is divisible by all terms in an expression.

Substitution

The word substitute comes up in everyday life. For example, if you order shopping, and the supermarket is out of stock for a particular item, you may receive a like-for-like substitute. The word substitute means to replace, and in maths, we specifically replace numbers for letters. For example, if we have the expression x+3 and are told that x=2, we can replace x with the number 2 and obtain a value. 

Prior knowledge

Key Terms

  • Substitute: To replace a number with a letter.

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