Rich example

## Warm-up

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.

$2x^2$
$-12$

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. $(px+r)(qx+s)$

How could this help in factorising quadratics?