This document was converted from Google Docs to Microsoft Word Format with XML Format (.docx)(not to be confused with .doc which is Office 97-2003 format) and then to unfiltered HTML (.html). It does look pretty good but there are always things to note when you're working off something like this. Firstly, the source for this is a HTML document instead of GFM so it's not human-readable. Secondly, `jekyll build` seems to not like the Therefore sign and has changed anything in a container with it to Times New Roman. I'm not sure how this actually translates on the remote repo but that's what I'm getting locally. The Google Docs version of this is much better anyway:

## Expand: Binomial Products

 FORMULA RULE EXAMPLE (a+b)(c+d) = ac+ad+bc+bd Use FOIL (3x + 5)(2x + 3) = 6x²+ 6x + 10x + 15 = 6x² + 16x + 16

## Expand: Perfect Squares

 FORMULA RULE EXAMPLE (a+b)2 or (a+b)(a+b) = a2+2ab+b2 Square the first 2x the product of the middle Square the last (2x - 3)² = 4x² - 12x + 9

## Expand: Difference of Two Squares

 FORMULA RULE EXAMPLE (a+b)(a-b) = a²–b² Square the first minus square the last (3x + 2y)(3x - 2y) = 9x² - 4y²

## Factor: Difference of Two Squares

 FORMULA RULE EXAMPLE a²-b² = (a+b)(a-b) Find the root of b term and solve as shown in the formula x² - 9 = (x+3)(x-3)

## Quick Note: Factoring

 FORMULA EXPLANATION EXAMPLE a(b-c) = -a(c-b)   Also consider:       a(b-c) = -a(c-b) = -a(-b+c) Essentially is the inverse operation of the brackets, flipping the terms around. Used to help simplify. x(x-5) - 2(5-x) = x(x-5) - 2(-x+5) = x(x-5) + 2(x-5) = (x-5)(x+2)

## Quick Note: Difference of Two Squares

 FORMULA RULE EXAMPLE x²–(a+b)² = (x-(a+b))(x+(a+b)) = (-a)(x+a+b) NA 4–(x+2)²  = (2–(x+2))(2+(x+2)) = (-x)(2+x+2) = -x(x+4)

## Factor: Monic Trinomials

 FORMULA RULE EXAMPLE Where p and q are factors of c that add to make b      x²+bx+c = (x+p)(x+q)   Note: px + qx = bx    ∴ p + q = b pq = c Find two integers that multiply to c and add to b   then write it in the form (x+p)(x+q) where p and q are the two numbers. x²+9x+20 =(x+4)(x+5)

## Expand into a Monic Trinomial

 FORMULA RULE EXAMPLE (x+a)(x+b) = x²+ax+bx+ab = x²+x(a+b)+ab =  x²+bx+c Use FOIL Factorise the middle terms (x+5)(x+3) = x²+3x+5x+15 = x²+x(3+5)+15 = x²+8x+15

## Grouping in Pairs

 FORMULA RULE EXAMPLE Where p and q are integers that add to ab and multiply to c:      x²+ax+bx+c =  x(x+p)+q(x+p) =  (x+p)(x+q) Group the 4 terms into pairs and take out the common binomial factor   *Also read Expand into a Monic Trinomial x²+4x+3x+12 = x(x+4)+3(x+4) = (x+4)(x+3)

## Factor: Non-Monic Trinomials

 FORMULA RULE EXAMPLE Where p and q are integers that add to b and multiply to ac   ax²+bx+c = ax²+px+qx+c = (ax+p)(a+q) Non-monic trinomial: ●     Coefficient of x² is not 1 ●     No common factors between the terms   Look for factors of ac that add to b Split the b term Factor in pairs 2x2+3x+2 = 2x2+1x+2x+2 = (2x+1)(x+2)

 FORMULA RULE/EXPLANATION EXAMPLE (x+p)(x+q) (x+p) = 0 or (x+q) = 0 ∴ x = -p or -q See rule for explanation The Null Factor Law states:   If ab=0, then a=0 or b=0. ∴ We can solve a quadratic in binomial form in stating that:    (x+5)(x-9) ∴ x = -5 or +9 (x+4)(x-9) ∴x = -5 or +9

## Quick Note: Indices

##### I know that this cheat sheet is Quadratics but I also forget a few indices things so I’m putting this here anyway and you can’t do anything about it.

 RULE/EXPLANATION EXAMPLE Multiplying: Keep the base, add the powers Dividing: Keep the base, subtract the powers Power to a power: Keep the base, multiply the powers Power of zero: x0 = 1, where x is any number Negative indices: a-m = 1/ Make sure that for any negative indices, you move them Fractional indices = the root x²x x³= x5 x6 ÷ x4 = x2 (x2)3 = x6 x-9 = 1/x9   x1/2 = √x x3/5 = 5√x3