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Topic: Algebraic Manipulation and Formulae (Higher - Unit 3)

Specification References: N5.1h N5.1h Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors. Multiply two linear expressions.

Candidates should be able to:

• understand that the transformation of algebraic expressions obeys and generalises the rules of generalised arithmetic
• manipulate an expression by collecting like terms
• multiply a single term over a bracket, e.g. a(b + c) = ab + ac
• write expressions to solve problems
• write expressions using squares and cubes
• factorise algebraic expressions by taking out common factors
• know the meaning of 'simplify', e.g. Simplify 3x - 2 + 4(x + 5)
• know the meaning of and be able to factorise, e.g.
  Factorise 3x²y - 9y
  Factorise 4x² + 6xy
• expand the product of two linear expressions, e.g. (2x + 3)(3x – 4)

Examples

1. This rectangle has dimensions as shown.
   
   Write down an expression in terms of x for
   1. the perimeter
   2. the area

        

         The perimeter of the rectangle is 68 centimetres.
         Use this information to form and solve an equation to work out the dimensions
         of the rectangle.

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