How do I expand a factorised equation?
Firstly put the equation into the the form (x+a)(x+b) this will make things easier later on.
Therefore, an equation such as (x+1)2 would become (x+1)(x+1)
Next expand the brackets. To do this simply multiply the first number in the first bracket, by the first number in the second bracket. Then multiply the second number in the first bracket by the second number in the second bracket. Then multiply together the second number in the first bracket by the first number in the second bracket. Finally multiply the first number in the first bracket with the second number in the second bracket.
This is much easier to see through working...
(x+1)(x+1)
1. xx = x2
2. 11 = 1
3. x1 = x
4. x1 = x
The last stage is to add all of this working together. This gives x2+x+x+1 which can be simplified to x2+2x+1.
Or...
(x+a)(x+b)
1. xx = x2
2. ab = ab
3. ax = ax
4. bx = bx
= x2+ax+bx+ab. In this example a and b would both be integers.
And that's how to expand a factorised number.
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Factorise and solve: x^2 - 8x = -15