Expanding and factorising · Grade 9

In Grade 9 you learn: expanding double brackets and factorising quadratics.

Expanding removes brackets by multiplying every term inside by what is outside. Factorising does the opposite: it puts brackets back in by taking out common factors. Both are everyday tools for simplifying algebra and solving equations.

Key facts

  • Expand a single bracket by multiplying every term inside: 3(2x − 5) = 6x − 15.
  • Expand two brackets by multiplying each term in the first by each term in the second (FOIL or a grid): (x + 2)(x + 5) = x² + 7x + 10.
  • (a + b)² = a² + 2ab + b² — not a² + b².
  • Factorise fully by taking out the highest common factor of the numbers and letters: 6x² + 9x = 3x(2x + 3).
  • To factorise x² + bx + c, find two numbers that multiply to c and add to b.

Worked examples

Example 1

Expand (x + 4)(x − 7).

Answer: x² − 3x − 28

Example 2

Factorise x² − x − 12.

Answer: (x − 4)(x + 3)

Example 3

Factorise 3x² + 10x − 8.

Answer: (3x − 2)(x + 4)

Other years