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

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.


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