### 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)
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://www.smore.com/7m5hu", "fetch_time": 1524319487000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2018-17/segments/1524125945222.55/warc/CC-MAIN-20180421125711-20180421145711-00081.warc.gz", "warc_record_offset": 869445619, "warc_record_length": 12660, "token_count": 597, "char_count": 1962, "score": 4.65625, "int_score": 5, "crawl": "CC-MAIN-2018-17", "snapshot_type": "longest", "language": "en", "language_score": 0.8250375390052795, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00033-of-00064.parquet"}