How can you factorise x^2-9
First, we notice how there is only an 'x2' term and a number in this expression. Also notice that the number, 9, is a square number. Whenever you have an expression that looks like 'x2-(any square number)' it can be factorised by completing the square. To complete the square, you take the square root of the number in the question. Remember that there will be a positive and a negative square root, so here the roots of 9 will be 3 and -3. Then you can factorise the expression like so:x2-9=(x+3)(x-3)Notice how each bracket contains an x and one of the square roots? This works because when you multiply out the brackets, you get x2-3x+3x-9. The 3x and -3x cancel each other out, leaving you with your original expression.
