In this resource, we are going to explore a method for factorising quadratic expressions using multiplication grids. We begin with a warm-up activity, which explores multiplication grids and builds up some of the ideas required for the factorising problem.

This multiplication grid for expanding \((x+4)(2x-3)\) is partially filled in. Fill in the rest of the grid to expand the brackets.

\(2x^2\) \(+8x\)
\(-3x\) \(-12\)

Therefore \((x+4)(2x-3) = 2x^2+8x-3x-12 = 2x^2+5x-12\).

What patterns do you notice in the grids as you expand the following brackets using this method?

  1. \((x+5)(x+2)\)

  2. \((x-1)(2x+3)\)

  3. \((2x-3)(3x-2)\)

  4. \((px+r)(qx+s)\)

  • There seem to be some common factors in some of the rows and columns.

  • There seems to be some relationship between the two diagonals in each grid.

How could this help in factorising quadratics?