Higher Tier Expessions

Students learn how to expand and factorise algebraic linear and quadratic expressions.  Learning progresses to expanding cubic and factorising quadratics in the form ax2 +bx + c.

This unit takes place in Term 2 of Year 9 and is followed by solving equations.


Expanding and Factorising Expressions
Revision Lessons
Prerequisite Knowledge

Use and interpret algebraic notation, including:

  • ab in place of a × b
  • 3y in place of 3 × y
  • a2 in place of a × a, a3 in place of a × a × a and a2b in place of a × a × b
  • a/b in place of a ÷ b
  • Coefficients written as fractions rather than decimals
Success Criteria

simplify and manipulate algebraic expressions by:

  • Multiplying a single term over a bracket
  • Taking out common factors
  • Expanding products of two or more binomials
  • Factorising quadratic expressions of the form (a)x2 + bx + c, including the difference of two squares
  • Simplifying expressions involving sums, products and powers including the laws of indices
Key Concepts
  • Students need to appreciate that writing with algebra applies the rules of arithmetic to unknown numbers which are represented as letters.
  • It is important to define the difference between an expression, equation and formula.
  • Linear (x), quadratic (x2) and cube terms (x3)cannot be collected together.
  • Understanding quadratics in the general form x2 + bx + c helps to factorise and expand expressions.
  • Developing mental methods to factorise quadratics is key to gaining confidence with quadratics equations later on.
Common Misconceptions
  • When multiplying out brackets students incorrectly forget to multiply the second term especially with negative products. E.g., 2(x + 5) = 2x + 10 and -2(x + 5) = -2x – 10
  • When factorising expressions a common misconception is to not fully factorise. E.g., 18x + 24y can be written as 9x + 12y
  • When expanding the product of two or more brackets students often incorrectly collect the like terms associated to the linear unknown

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Problem Solving with Averages

Students are challenged to apply their understanding of the mean, mode, median and range to calculate datasets by setting up and solving equations.

Problem Solving with Compound Percentages

Five, real-life and functional problem solving questions on compound percentage changes.

Pull Up Nets

Home learning project teaching how to create pull up nets for 3D shapes.