Higher Tier Expessions

Expanding Brackets

Factorising Terms

Expanding Quadratics

Factorising Expressions with Powers

Factorising Quadratics

Factorising Quadratics ax² + bx + c

Expanding Cubic 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.