[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-397405-105":59,"doc-detail-397405-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","algebra-cheat-sheet","Algebra Cheat Sheet","","Algebra cheat sheet covering key fundamentals and formulas for solving and transforming expressions. Includes arithmetic properties of factoring, exponent rules, radical properties, inequality and absolute value properties, and the distance formula. Provides complex number operations and logarithm definitions with log rules. Also summarizes common factoring identities, the quadratic formula, completing the square, solving absolute value equations/inequalities, and core function and graph forms such as linear, quadratic, circle, ellipse, and hyperbola, plus frequent algebra errors with corrections.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/algebra-cheat-sheet/397405/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/algebra-cheat-sheet/397405.png","ImageObject",300,407,{"name":92,"@type":93},"Muffet","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-26",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are the key exponent and radical properties included in the cheat sheet?","Question",{"text":113,"@type":114},"The sheet lists standard exponent rules like a^(n+m)=a^n·a^m and (a^n)^m=a^(nm), plus radical relationships for odd/even indices and simplification patterns.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the cheat sheet define and use logarithms?",{"text":118,"@type":114},"It states y=log_b(x) is equivalent to x=b^y, gives common examples like log_5(125)=3, and provides core log identities for products, quotients, and powers, along with the domain x>0.",{"name":120,"@type":111,"acceptedAnswer":121},"What formulas are given for solving quadratic equations and related problems?",{"text":122,"@type":114},"It includes the quadratic formula for ax^2+bx+c=0, instructions for completing the square, and absolute value equation/inequality solution rules using |p| forms.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},397405,1790693202,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":52,"preview_page_count":4},962090768927,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Basic Properties and Facts  \nArithmetic Operations  \nab + ac = a (b + c)  \n 􀀐 ab 􀀑 =  a c bc  \na b  \n+  \nc   ad + bc =  \nd bd  \na 􀀀 b  b 􀀀 a  \n=  \nc 􀀀 d d 􀀀 c  \nab~~ ~~+a~~ ~~ac = b + c; a  0  \nExponent Properties  \nanam = an+m (an )m = anmaanm = an􀀀m = a1m􀀀na ~~n~~m = 􀀐 a ~~1~~m 􀀑 n = (an )~~1~~m  \n􀀐 ab􀀑 􀀀n = 􀀒 ba􀀓 n = bann  \nProperties of Radicals  \npn a = a ~~1~~n pn ab  \nmp pn a = na rn ab pn an = a if n is odd pn an = jaj if n is even  \na 􀀒 bc􀀓 = abc  \n a   ac =  \n􀀒 bc 􀀓 b  \na  c   ad 􀀀 bc 􀀀 =  \nb d bd  \na + b  \nc  \n= ac +  \nb c  \n 􀀐 ab 􀀑   ad  \n􀀐 cd 􀀑 = bc  \n(ab)n = an bna0 = 1 , a  0 􀀐 ab􀀑 n = abnnan = an  \na􀀀n = a1n  \n= pn apn b  \n=  \npn a  \npn b  \nProperties of Inequalities  \nIf a \u003C b then a + c \u003C b + c and a 􀀀 c \u003C b 􀀀 c  \na  b  \nIf a \u003C b and c > 0 then ac \u003C bc and \u003C  \nc c  \na  b  \nIf a \u003C b and c \u003C 0 then ac > bc and >  \nc c  \nProperties of Absolute Value  \njaj = ( 􀀀 aa f af a  00  \nja j 􀀕 0 j􀀀aj = ja j  \n􀀌 a 􀀌  j a j jabj = ja j j bj 􀀌 􀀌 =  \n􀀌 b 􀀌 j bj  \nja + bj 6 jaj + j bj Triangle Inequality  \nDistance Formula  \nIf P1 = (x1 ; y 1 ) and P2 = (x2 ; y2 ) are two points the distance between them is  \nd (P1 ; P2 ) = q (x2 􀀀 x1 )2 + (y2 􀀀 y1 )2  \nComplex Numbers  \ni = p􀀀1 i2 = 􀀀1 p􀀀a = ipa , a 􀀕 0  \n(a + bi) + (c + di) = a + c + (b + d)i  \n(a + bi) 􀀀 (c + di) = a 􀀀 c + (b 􀀀 d) i (a + bi) (c + di) = ac 􀀀 bd + (ad + bc) i (a + bi) (a 􀀀 bi) = a2 + b2  \nja + bij = pa2 + b2 Complex Modulus  \n(a + bi) = a 􀀀 bi Complex Conjugate (a + bi) (a + bi) = ja + bij2  \n© October 2025 Paul Dawkins-[https://tutorial.math.lamar.edu](https://tutorial.math.lamar.edu)  \nLogarithms and Log Properties  \nDefinition  \ny = logb(x) is equivalent to x = by  \nExample  \nlog5 (125) = 3 because 53 = 125  \nSpecial Logarithms  \nln (x) = loge(x) natural log log (x) = log 10 (x) common log where e = 2:718281828 : : :  \nLogarithm Properties logb(b) = 1  \nlogb(bx ) = x  \nlogb(1) = 0 blog b(x) = x  \nlogb (xr ) = r logb(x)  \nlogb (xy) = logb(x) + logb(y) logb 􀀒 xy􀀓 = logb(x) 􀀀 logb(y) The domain of logb(x) is x > 0  \nFactoring and Solving  \nFactoring Formulas  \nx2 􀀀 a2 = (x + a) (x 􀀀 a) x2 + 2ax + a2 = (x + a)2  \nx2 􀀀 2ax + a2 = (x 􀀀 a)2  \nx2 + (a + b)x + ab = (x + a) (x + b) x3 + 3ax2 + 3a2 x + a3 = (x + a)3  \nx3 􀀀 3ax2 + 3a2 x 􀀀 a3 = (x 􀀀 a)3  \nx3 + a3 = (x + a) 􀀀x2 􀀀 ax + a2 􀀁  \nx3 􀀀 a3 = (x 􀀀 a) 􀀀x2 + ax + a2 􀀁 x2n 􀀀 a2n = (xn 􀀀 an ) (xn + an ) If n is odd then,  \nxn 􀀀 an = (x 􀀀 a) 􀀀xn􀀀1 + axn􀀀2 + 􀀁 􀀁 􀀁 + an􀀀1􀀁 xn + an =  \n(x + a) 􀀀xn􀀀1 􀀀 axn􀀀2 + a2 xn􀀀3 􀀀 􀀁 􀀁 􀀁 + an􀀀1􀀁  \nQuadratic Formula  \nSolve ax2 + bx + c = 0 , a  0  \nx =  \n􀀀b 􀀆pb2 􀀀 4ac  \n2a  \nIf b2 􀀀 4ac > 0 – Two real unequal solns. If b2 􀀀 4ac = 0 – Repeated real solution. If b2 􀀀 4ac \u003C 0 – Two complex solutions.  \nSquare Root Property  \nIf x2 = p then x = 􀀆pp  \nAbsolute Value Equations/Inequalities  \nIf b is a positive number  \njpj = b ) p = 􀀀b or p = bjpj \u003C b ) 􀀀b \u003C p \u003C b  \njpj > b ) p \u003C 􀀀b or p > b  \nCompleting the Square  \nSolve 2x2 􀀀 6x 􀀀 10 = 0  \n(1) Divide by the coefficient of the x2  \nx2 􀀀 3x 􀀀 5 = 0  \n(2) Move the constant to the other side.  \nx2 􀀀 3x = 5  \n(3) Take half the coefficient of x, square it and add it to both sides  \nx2 􀀀 3x + 􀀒 􀀀 32􀀓 2 = 5 + 􀀒 􀀀 32􀀓 2 = 5 + 94 = 294  \n(4) Factor the left side  \n􀀒x 􀀀 32􀀓 2 = 294  \n(5) Use Square Root Property x 􀀀 32 = 􀀆 r ~~ ~~294 = 􀀆 ~~ ~~p~~ ~~292  \n(6) Solve for x  x = 32 􀀆 p~~ ~~292  \n© October 2025 Paul Dawkins-[https://tutorial.math.lamar.edu](https://tutorial.math.lamar.edu)  \nFunctions and Graphs  \nConstant Function  \ny = a or f (x) = a  \nGraph is a horizontal line passing through the point (0; a) .  \nLine/Linear Function  \ny = mx + b or f (x) = mx + b  \nGraph is a line with point (0; b) and slope m.  \nSlope  \nSlope of the line containing the two points (x1 ; y 1 ) and (x2 ; y2 ) is  \nm =  \ny2 􀀀 y 1 x2 􀀀 x 1  \n=  \nrise  \nrun  \nSlope – intercept form  \nThe equation of the line with slope m andy-intercept (0; b) is  \ny = mx + b Point – Slope form  \nThe equation of the line with slope m and  \npassing through the point (x1 ; y 1 ) is y = ","cbCainSW0TM4IWuB","https://ap.wps.com/l/cbCainSW0TM4IWuB","pdf",191189,"English","# Basic Properties and Facts\n# Arithmetic, Exponents, Radicals\n# Inequalities and Absolute Value\n# Distance Formula and Complex Numbers\n# Logarithms and Log Properties\n# Factoring and Solving\n# Functions and Graphs\n# Common Algebraic Errors","[{\"question\":\"What are the key exponent and radical properties included in the cheat sheet?\",\"answer\":\"The sheet lists standard exponent rules like a^(n+m)=a^n·a^m and (a^n)^m=a^(nm), plus radical relationships for odd/even indices and simplification patterns.\"},{\"question\":\"How does the cheat sheet define and use logarithms?\",\"answer\":\"It states y=log_b(x) is equivalent to x=b^y, gives common examples like log_5(125)=3, and provides core log identities for products, quotients, and powers, along with the domain x\\u003e0.\"},{\"question\":\"What formulas are given for solving quadratic equations and related problems?\",\"answer\":\"It includes the quadratic formula for ax^2+bx+c=0, instructions for completing the square, and absolute value equation/inequality solution rules using |p| forms.\"}]","Algebra Cheat Sheet | PDF",1790461558]