Question: Factorise the expressions: 1. X^2 - 9 2. 2X^2 - 14X + 24

The ways to complete the first one is to realise that it involves a difference of two squares. If you were to see (X^2) with a constant (number), you know they have no factor in common, meaning the two terms (X^2) and (9) have nothing the same. After this realisation you should expand and factorise the expression by realising that (-9) can be made from (-3) and (+3). This leads to the answer ((X+3)(X-3)). The question can be reverse engineered from the answer.For this you should notice that all the terms have a factor in common, in this case it is (2) so pull it out of the expression (2(X^2 - 7X + 12)). After this, the expression is much simpler, all that is required is to find two numbers that add to make (-7) and multiply to make (12). In this case the numbers are (-3) and (-4) leading to (2(X^2 - 4X - 3X + 12)). Writing down this step may be confusing so it can often be skipped. The final step is to factorise, the answer is (2(X - 4)(X - 3)).