### Alerbra Guide sheet

-has the highest degree of 2

-graphed as a parabola

## How to Expand and simplify :

EXAMPLE: the equations seen below is in factored form expand and simplify.equation:y=a(x-r)a(x-s).

step1: First to expand you, apply everything directly in front of the bracket into every term inside the bracket.-y=a(x-r)a(x-s)-y=ax-ar+ax-s.

step2: You collect the like terms to simplify ,meaning collect everything that has the same components. (ex; coefficients,exponents ect)-y=ax-ar+ax-sy=2ax-ar-s.

step3: Leave what ever cannot be collected and simplified and just add them into the equation.

## How to Compleate a Square:

(Ax2+Bx+C)- Referance Equation.step1:Block off the first two terms. 1)y= 2x2+8x-3 then... y= (2x2+8x)-3.

step2: Factor out the A value. 2)y=2(x^2+4x)-3. (note : when you factor out the A you divde the middle term by it.)

step3:To find your zeros didvide te middle term by two the square it .y=2(x2+4x+4-4)-3.

step4:Take the negative out then solve the ending and divide the equation by two. 4)y=2(x+2x)2-11.(note:when you take the negative out multiply it by the first term "A" then take out the positive zero and bring the square root to the end bracket.)

## Factoring

There are many ways of factoring here are just SOME ways!

GOLDEN RULE:

-always look for a common factor

-then check if it can be factored any more

-Difference of squares.

here is an example: x^2-9 (you would square both terms)

another example is: (x+5)(x-5)

these are the two types!

-Decomposition.

here is an example: 2x^2+5x-7

-start off by solving for the product and the sum for the middle term and replace it: 2x^2+7x-2x-7

-then factor out common terms :x(2x+7)-1(2x+7)

- then simplify even more (2x+7)(x-1)

-By Grouping

here is an example: x^3+2x^2+8x+16

-the first thing to do would be to block off each two terms then factor out what ever is in each bracket x^2(x+2)(X^2+8)

-then factor/simplify the rest! (x+2)(x^2+8)