Section outline

  • Outcomes

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    In this course you will learn about:

    1. Identifying and writing algebraic expressions.
    2. Recognising and working with like and unlike terms.
    3. Simplifying algebraic expressions.
    4. Solving linear equations.

  • What is an algebraic expression?

    Algebraic expressions are made by replacing sentences with numbers, symbols and letters.  For example, a number increased by \(5\) and then divided by \(2\) is written algebraically as; \( \frac{x+5}{2} \). In this mathematical form you can see that algebraic expressions are a universal language where symbols and letters can be translated to any language.

    Each part of an algebraic expression has a special name. The next video explains what variables, constants, coefficients and terms are.  

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      Degree of an algebraic expression

      The degree of an algebraic expression with a single variable is the highest exponent of that variable. For example, the degree of the expression \( { x}^{3} \)\(+\)\( x\)\(-4\) is \(3\).

      You can also find the degree of an algebraic expression with more than one variable. The degree of an expression with more than one variable is the highest sum of the powers of the variables. The degree of \( { x}^{3} {y}^{4}\)\(+\)\( x\)\({y}^{2}\)\(-xy\) is \(7\). [edit: I suggest removing the above link to the quiz below - it's not necessary]

    • Find the degree Quiz
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  • Working with like and unlike terms

    Like and unlike are not only actions for Facebook posts. In Maths, only like terms can be combined when adding or subtracting algebraic expressions. Like terms have the same variables, raised to the same power and it is only the coefficients that are different. 

    Example

    \( { x}^{2} \) and \(-2\)\( { x}^{2} \) are like terms because they have the same variable raised to the same power.

    \( { x}^{2} \) and \(-2\)\( { x}^{3} \) are unlike terms because the variable has different exponents.

    Try the next exercise to test your understanding of like terms.

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      Exercise: Like or unlike?


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      Collecting like terms

      We can add and subtract like terms to simplify or shorten an algebraic expression. 

      3x cubed and 5 x cubed are like terms and 4 x y and 6 y x are like terms

      When you add or subtract like terms, the variables and exponents in the terms don't change. You only need to add/subtract the coefficients. 

      We can rewrite \(-3 { x}^{3}+4xy-5{x}^{3}+6yx\) as \(-8{x}^{3}+10xy\) by collecting the like terms.

      For more examples on adding like terms watch the next video. 

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      Exercise: Combining like terms

      The more you practise, the quicker you will become at adding and subtracting like terms. Practise your skills by doing this exercise, Combining like terms.

  • Simplify algebraic expressions

    We often simplify an algebraic expression to make it easier to work with or calculate or to use in some other way. The following words are used to describe specific expressions that you will come across often and you need to learn the definition of. Click on each word to learn more.

    Monomial
    Binomial
    Trinomial
    Polynomial

    Remember that: Mono=one, bi=two, tri=three and poly=many.

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      Multiplying a monomial by a binomial

      We use the properties of real numbers to multiply algebraic expressions. The following video explains how to multiply a single term into a bracket. Make sure you understand how to simplify exponents before continuing with the next video. 

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      Multiplying a binomial with a binomial

      Remember that a binomial consists of two terms. The steps for multiplying a binomial by another binomial are explained in detail in the next video. Make sure to pause when requested and try the example for yourself. 


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      Exercise: Find the products

      Practise the methods you have just learnt for finding products by trying this next exercise: Multiply binomials. 

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      Substitution 

      In algebra replacing letters with numbers is called substitution. For example, if you replace \(a\) with \(4\) in the expression \(a+3\) the you will get \(4+3=7\). If you need more practise with this concept then watch the next video. 

    • Activity: Algebraic expressions Interactive Content
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  • Solve linear equations

    An algebraic equation is made up of algebraic expressions separated by an equal sign. For example, \(2x-1=3+x\) is an equation, which shows that the algebraic expressions \(2x-1\) and \(3+x\) are equal. When the power of the variable in the equation is \(1\) then the equation is called a linear equation.

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      Solve equations by inspection

      Some equations are simple enough that they can be solved by inspection. This is explained in the next video. 

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      Solve equations using inverse operations

      The "golden rule" of algebraic equations is, whatever you do to one side of the equation, you must do to the other side. The equation must be balanced at all times.

      So, if you add, subtract, multiply or divide on one side of the equation, you must do the same to the other side to keep the equation balanced. In the next video, solving equations using inverse operations to keep the equation balanced is explained. 

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      Exercise: Solving linear equations

      Try these exercises to test your knowledge on linear equations: Reasoning with linear  equations AND Multi-step equations. 

    • Attribution & licence Page
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