[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-508189-105":59,"doc-detail-508189-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","factoring-special-products-pert-math-section-84","Factoring Special Products - PERT Math Section 8.4","","Factoring Special Products practice for PERT Math Section 8.4 focuses on recognizing polynomial patterns and factoring by grouping like terms. Problems emphasize using exponent rules when bases match, then verifying factorizations by multiplying back. Includes quick review guidance, a set of algebra and word problems, and an answer key with step-by-step reasoning using difference of squares and perfect-square trinomials. Suitable for independent practice after worksheet topics.",{"@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/factoring-special-products-pert-math-section-84/508189/",{"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/factoring-special-products-pert-math-section-84/508189.png","ImageObject",300,407,{"name":92,"@type":93},"Sophia Brooks","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-05",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What strategies are used to factor special products in this worksheet?","Question",{"text":113,"@type":114},"The worksheet emphasizes pattern recognition, keeping like terms together, applying exponent rules when bases match, and checking factorization by multiplying the factors back together.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you factor expressions like a difference of squares?",{"text":118,"@type":114},"Use the difference-of-squares pattern: when a perfect square minus another perfect square is present, it factors into two binomials.",{"name":120,"@type":111,"acceptedAnswer":121},"What does the answer key provide for the practice problems?",{"text":122,"@type":114},"The answer key lists factored forms for each numbered problem and identifies when expressions cannot be factored over the real numbers.","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},508189,1791376945,{"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":81,"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":39,"preview_page_count":4},962084925636,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Practice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nFactoring Special Products  \nPERT Math 􀀏 Section 8.4  \n\n| Name:   | D | ate:   | S | core:   / 12 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nPolynomial work is pattern work. Keep like terms together, apply exponent rules only when the bases match, and check factoring by multiplying the factors back together.  \n▷ Example: Factor x2 + 9x + 20 .  \nWork: Look for two numbers that multiply to 20 and add to 9. The numbers are 4 and 5.  \n⋆ Answer: (x + 4)(x + 5)  \n♦ Practice Problems  \nSolve each problem. Show enough work that another student could follow your thinking.  \n1. Factor x2 􀀀 36. 6. Factor 16m2 + 40m + 25 .  \n2. Factor 4x2 􀀀 81. 7. Factor 49p2 􀀀 64.  \n3. Factor x2 + 12x + 36 .  \n8. Factor x2 􀀀 18x + 81 .  \n4. Factor 9a2 􀀀 24a + 16 .  \n9. Factor 36r2 + 12r + 1 .  \n5. Factor 25y2 􀀀 1.  \n10. Is x2 + 25 factorable over the real numbers?  \n♦ Word Problems  \n11. A square area is x2 + 14x + 49 . Factor to 􀀂nd side length.  \n12. A border area uses y 2 􀀀 100. Factor it.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \n1.  (x 􀀀 6)(x + 6)  7.  (7p 􀀀 8)(7p + 8)   \n2. (2x 􀀀 9)(2x + 9) 8.  (x 􀀀 9)2   \n3.  (x + 6)2  9.  (6r + 1)2   \n4.  (3a 􀀀 4)2  10. No  \n5.  (5y 􀀀 1)(5y + 1)  11. (x + 7)2 ; side x + 7  \n6.  (4m + 5)2  12.  (y 􀀀 10)(y + 10)   \nStep-by-Step Explanations  \n1. Two squares with a subtraction sign means split into a sum and difference.  \n2. Both 4x2 and 81 are perfect squares, so the difference-of-squares pattern  \n􀀂ts.  \n3. The ends square nicely and 12x is twice x times 6—that makes it a perfect square.  \n4. Since 9a2 and 16 are squares and 􀀀24a is twice their product, fold it into a square.  \n5. This is (5y)2 􀀀 12 , so the difference of squares splits it apart.  \n6. It lines up with (a + b)2 : 4m and 5 squared, with 40m as twice their product.  \n7. Recognize (7p)2 􀀀 82 and let the difference-of-squares rule do the work.  \n8. Check the middle: twice x times 􀀀9 is 􀀀18x, con􀀂rming a perfect-square trinomial.  \n9. Both ends are squares and 12r equals 2(6r)(1), so it collapses to one square.  \n10. This is a sum of squares, and that pattern simply doesn’t factor with real numbers.  \n11. The trinomial is a perfect square, so the side length is just x + 7 .  \n12. Spot y2 􀀀 102 and apply the difference-of-squares pattern directly.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](","cbCaipZp4z10VC7E","https://ap.wps.com/l/cbCaipZp4z10VC7E","pdf",101913,"English","# Quick Review and Helpful Hints\n# Practice Problems\n# Word Problems\n# Answer Keys\n# Step-by-Step Explanations","[{\"question\":\"What strategies are used to factor special products in this worksheet?\",\"answer\":\"The worksheet emphasizes pattern recognition, keeping like terms together, applying exponent rules when bases match, and checking factorization by multiplying the factors back together.\"},{\"question\":\"How do you factor expressions like a difference of squares?\",\"answer\":\"Use the difference-of-squares pattern: when a perfect square minus another perfect square is present, it factors into two binomials.\"},{\"question\":\"What does the answer key provide for the practice problems?\",\"answer\":\"The answer key lists factored forms for each numbered problem and identifies when expressions cannot be factored over the real numbers.\"}]","Factoring Special Products - PERT Math Section 8.4 | PDF",1791212330]