[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-207494-105":3,"detail-sidebar-cat-0-en-105":75,"doc-detail-207494-en":125},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":68,"head_meta":70,"extra_data":72,"updated_unix":74},105,"en","aqa-gcse-further-maths-algebra-toolkit-expanding-factorising","AQA GCSE Further Maths - Algebra Toolkit - Expanding & Factorising","","AQA GCSE Further Maths Algebra Toolkit focuses on mastering expanding and factorising algebraic expressions. Covers expanding single and double brackets, multiplying all terms, simplifying results, handling negatives carefully, and using common factor methods. Includes guidance on factorising fully using highest common factors, index laws, and working with brackets in factors. Extends to expanding triple brackets with grid methods and shows worked examples, plus factorising by grouping with common brackets.",{"@graph":14,"@context":67},[15,34,50],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/aqa-gcse-further-maths-algebra-toolkit-expanding-factorising/207494/",4,{"url":32,"name":10,"@type":35,"author":36,"headline":10,"publisher":39,"fileFormat":42,"inLanguage":8,"description":12,"dateModified":43,"datePublished":44,"encodingFormat":42,"isAccessibleForFree":45,"interactionStatistic":46},"DigitalDocument",{"name":37,"@type":38},"Himbo","Person",{"url":19,"name":40,"@type":41},"DocShare","Organization","application/pdf","2026-09-06","2026-09-05",true,{"@type":47,"interactionType":48,"userInteractionCount":22},"InteractionCounter",{"@type":49},"ViewAction",{"@type":51,"mainEntity":52},"FAQPage",[53,59,63],{"name":54,"@type":55,"acceptedAnswer":56},"How do you expand single brackets in further maths?","Question",{"text":57,"@type":58},"Multiply every term inside the bracket by the term outside the bracket, then simplify and collect like terms.","Answer",{"name":60,"@type":55,"acceptedAnswer":61},"What is the key idea behind factorising out a term from an expression?",{"text":62,"@type":58},"Factorising is the opposite of expanding: find the highest common factor of each term and place it outside a bracket, then determine what multiplies back to each term.",{"name":64,"@type":55,"acceptedAnswer":65},"How do you expand three brackets efficiently?",{"text":66,"@type":58},"Expand two brackets first, simplify, rewrite as a single long bracket, then expand with the third bracket. A grid can help track all terms.","https://schema.org",{"og:url":32,"og:type":69,"og:title":10,"og:site_name":40,"og:description":12},"article",{"robots":71,"canonical":32},"index,follow",{"doc_id":73,"site_id":7},207494,1788599771,{"code":4,"msg":76,"data":77},"success",[78,82,86,89,94,99,104,109,114,117,121],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":79,"show_sort_weight":80,"slug":81},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":83,"show_sort_weight":84,"slug":85},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":87,"slug":88},70,"exam",{"id":90,"doc_module":4,"doc_module_name":25,"category_name":91,"show_sort_weight":92,"slug":93},5,"Comic",60,"comic",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},6,"Technology",50,"technology",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},7,"Healthcare",40,"healthcare",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},8,"Research & Report",30,"research-report",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},9,"Religion & Spirituality",20,"religion-spirituality",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":115,"show_sort_weight":112,"slug":116},"World Cup","world-cup",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":119,"show_sort_weight":118,"slug":120},10,"Lifestyle","lifestyle",{"id":122,"doc_module":4,"doc_module_name":25,"category_name":123,"show_sort_weight":90,"slug":124},19,"General","general",{"code":4,"msg":76,"data":126},{"doc_id":73,"user_id":127,"nickname":37,"user_avatar":128,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":129,"file_id":130,"file_url":131,"file_type":132,"file_size":133,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":97,"language":134,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":135,"faqs":136,"seo_title":137,"seo_description":12,"update_tm":74,"read_time":138},687197100911,"https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697","Head to www.savemyexams. com for more awesome resources  \n AQA GCSE Further Maths  \nAlgebra Toolkit  \nContents  \n Expanding & Factorising  \n Factorising Quadratics  \n Quadratics Factorising Methods  Completing the Square  \n Solving Quadratic Equations  Equating Coezcients  \n Forming & Solving Equations  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nExpanding & Factorising  \nBasic Expanding & Factorising How doI expand brackets?  \n Expanding brackets means multiplying all the terms inside a bracket by the term outside of the bracket  \n For GCSE Mathematics you will have learnt how to expand a single bracket  \n Multiply each term inside the bracket by the term outside the bracket  \n2x(3x − 4y + 5) = 2x × 3x − 2x × 4y + 2x × 5  \n= 6x2 − 8xy + 10x  \n You will also have learnt how to expand double brackets  \n You can turn this into two single brackets by multiplying each term inside one bracket by the other bracket  \n For Level 2 Further Mathematics you might get more than two terms in a bracket  \n Therefore using a grid or turning the expression into single brackets will be more helpful than  \nusing FOIL  \n(2x + 5)(3x − 4y + 5) = 2x(3x − 4y + 5) + 5(3x − 4y + 5)  \n= 6x2 − 8yx + 10x + 15x − 20y + 25  \n= 6x2 + − 8xy + 25x − 20y + 25  \n A bracket that is raised to the power of 2 can also be written as a double bracket  \n ( x + y + z) 2 = ( x + y + z) ( x + y + z)  \n Write as a double bracket and then expand  \n Do not just square each term inside the bracket  \n Be very careful when working with negatives  \n Remember to simplify expressions where possible How do I factoriseouta term from an expression?  \n Factorising is the opposite of expanding  \n Firstly |nd the highest common factor of each term in the expression and put this outside a bracket  \n The highest common factor could be a single number or a variable or both  \n 12x + 8 = 4 ( . . . + . . . )  \n 2x2 − 5x = x ( . . . − . . . )  \n 6x2 + 8xy + 4x = 2x( . . . + . . . + . . . )  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \n If the terms involve the same variable(s) to diyerent powers then the highest common factor will include the variable(s) with the smallest power  \n 4x5 + 5x4 = x4 ( . . . + . . . )  \n 6x4y 7 − 8x9y 5 = 2x4y 5 ( . . . − . . . )  \n The highest common factor could also contain brackets  \n ( x + 1)2 + 5( x + 1) = ( x + 1)( . . . + . . . )  \n ( x + 1)( x + 2)( x + 3) + ( x + 1)( x + 2)( x + 4) = ( x + 1)( x + 2)( . . . + . . . )  \n Then |nd what you need to multiply the highest common factor by to get each term  \n You might need to use the index law: xa × xb = xa +b  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \n Worked example  \n(a) Expand and simplify ( x + 4)( x4 − 5x3 + 4x2 − 7x) .  \nThe second bracket has more than two terms so turn the expression into single bracket expansions  \nCollect like terms  \n(b) Factorise fully ( x + 1)(2x + 3) + ( x + 1)( x − 2) .  \nThere are two terms in this expression;and  \nBoth contain the common factor  \nAs a bracket is a factor, using \" big square brackets \" can help keep track of what 's left  \nSimplify the \" big square brackets \"  \nThe whole expression is now fully simpli|ed (but it 's always worth checking!)  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \nExpanding Triple Brackets How doI expand three brackets?  \n Multiply out any two brackets using a standard method and simplify this answer (collect any like terms)  \n Replace the two brackets above with one long bracket containing the expanded result  \n Expand this long bracket with the third (unused) bracket  \n This step often looks like (x + a)","cbCaitTFMw8g7c9u","https://ap.wps.com/l/cbCaitTFMw8g7c9u","pdf",4335775,"English","# Contents\n## Expanding & Factorising\n### Expanding brackets\n### Factorising out the highest common factor\n### Expanding triple brackets\n### Factorising by grouping","[{\"question\":\"How do you expand single brackets in further maths?\",\"answer\":\"Multiply every term inside the bracket by the term outside the bracket, then simplify and collect like terms.\"},{\"question\":\"What is the key idea behind factorising out a term from an expression?\",\"answer\":\"Factorising is the opposite of expanding: find the highest common factor of each term and place it outside a bracket, then determine what multiplies back to each term.\"},{\"question\":\"How do you expand three brackets efficiently?\",\"answer\":\"Expand two brackets first, simplify, rewrite as a single long bracket, then expand with the third bracket. A grid can help track all terms.\"}]","AQA GCSE Further Maths - Algebra Toolkit - Expanding & Factorising | PDF",126]