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.

\(x\) | \(+4\) | |
---|---|---|

\(2x\) | \(2x^2\) | |

\(-3\) | \(-12\) |

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

\((x+5)(x+2)\)

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

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

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

How could this help in factorising quadratics?