Differernce of a square/inequalities (1 Viewer)

[davidbarnes]

Algebra stuffs me right up, and as i don't have the basics I get furthur behind.
Can anyone please explain "differernce of a square" and "inerqualities" to me, as though I knew nothing of these at all. Any help would be appreciated.

 

[SoulSearcher]

Difference of two squares: a² - b² = (a-b)(a+b)
You can check this by expanding the brackets.

Inequalities: things like x - 10 > 8 or 2x < 3x + 9.
Comes in two forms, greater than or less than, which are symbolised by the > and < signs respectively, and greater than and equal to or less than and equal to, characterised by the symbols > and < respectively.
You are basically solving for values of the pronumeral which the inequality is true for, for example in the first example,
x - 10 > 8, which is that x - 10 is greater than 8. To find the values of x for which this inequality is true, you add 10 to both sides, so:
x - 10 + 10 > 8 + 10
x > 18, which says for values of x larger than 18, the inequality is true.

 

[Darrow]

Ok, here is a nice way to do the completing the square:

with things such as:
x^2+4x=0

You divide the co-efficient of the bx (b being the number- so 4 in this case) by 2, then square it and add it to both sides.
So:
x^2 +4x +4 = 4
You can then 'complete the square' by using first term (so just x in this case) and the 1/2 4 that we used.
So, it becomes:
(x+2)^2=4
And there you go