In algebra, the opposite of expansion is factorisation. Let's have a look at it:
Factorising Quadratics (no coeficciant)
Here we have a basic expression: 8x + 4.
- Extract all the numbers from this expression. They will be 8 and 4 in this case.
- We first need to select the highest number that divides into both of them. In this example, that number is 4 and we can't go any higher than that.
- We can now safely say that 4 will be the number outside of our brackets. Our final expression now looks like this: 4( )
- What will be inside the brackets is what is left behind. When we divide 8 and 4 by 4, we get 2 and 1. We can put this in.
- Both of these numbers are positive, so our expression now looks like: 4(2 + 1).
- But we are not quite done yet because originally, our first number wasn't just 8, it was 8x, so we need to put this back in: 4(2x + 1).
- Bingo! We can check this by expanding it (dividing what's outside the brackets by what is inside) to get 8x + 4. Perfect!