Algebraic Expressions

Collecting Like Terms

Simplifying Products and Quotients

Substitution into Expressions

Expanding Brackets

Factorising Terms

Factorising Expressions with Powers

Expanding Quadratics

Factorising Quadratics

Simplifying Expressions

Expanding Brackets

Factorising Expressions

Expanding Quadratics

Factorising x^2 + bx + c

Prerequisite Knowledge

• use simple formulae
• generate and describe linear number sequences
• express missing number problems algebraically
• find pairs of numbers that satisfy an equation with two unknowns

Success Criteria

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
• brackets

simplify and manipulate algebraic expressions by:

• collecting like terms
• multiplying a single term over a bracket
• taking out common factors
• expanding products of two or more binomials
• factorising quadratic expressions of the form 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.
• The multiplication symbol is omitted when using algebraic notation to avoid confusion between and ×. Quotients are written as using simplified fractions.
• 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.

Common Misconceptions

• Students often forget ab = ba = a × b and b + a = + b when collecting like terms.
• 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.