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?
