{"book":"adl0258","page":207,"text":"۲۰۳\nمثال ۹ لا۴ - ۶لای + ۸ ی۲ -ع۲ + ۲ی ع را بمضروبات تفریق کنید\nجمله مفروضه = (لا۴ - ۶لای + ۹ ی۲) - (ی۲ + ع۲ - ۲ ی ع)\n=(لا۲-۳ی)۲ - (ی - ع)۲\n= {(لا۲-۳ی) + (ی - ع)}{(لا۲-۳ی) - (ی - ع)}\n= (لا۲-۲ی -ع)(لا۲-۴ی + ع)\nمثال ۱۰ (ا۲-ب۲)(لا۲-ی۲) + ۴ اب لای را بمضروبات تفریق کنید\nجمله مفروضه = ا۲لا۲ - ا۲ی۲ - ب۲لا۲ + ب۲ی۲ + ۴ ا ب لای\n= (ا۲لا۲ + ب۲ی۲ + ۲ ا ب لای) - (ا۲ی۲ + ب۲لا۲ - ۲ ا ب لای)\n= (الا + ب ی)۲ - (ای - ب لا)۲\n= {(الا + ب ی) + (ای - ب لا)}{(الا + ب ی) - (ای - ب لا)}\n= {(ا - ب) لا + (ا + ب) ی} {(ا + ب) لا - (ا - ب) ی}\nمثال ۱۱ لا۴ + ۶لا۳ + ۲لا۲ - ۱۵لا + ۶ را بمضروبات تفریق کنید\nجمله مفروضه = (لا۴ + ۶لا۳ + ۹لا۲) - (۵لا۲ + ۱۵لا) + ۶\n= (لا۲ + ۳لا)۲ - ۵(لا۲ + ۳لا) + ۶\n= {(لا۲ + ۳لا) - ۲}{(لا۲ + ۳لا) - ۳}\n= (لا۲ + ۳لا - ۲) (لا۲ + ۳لا - ۳)\nمثال ۱۲ لا۴ + ۲لا۳ی + ۳لا۲ی۲ + ۲لای۳ + ی۴ را بمضروبات تفریق کنید\nجمله مفروضه = (لا۴ + ۲لا۳ی + لا۲ی۲) + لا۲ی۲ + (۲لا۲ی + ۲ لای۳)\n= (لا۲ + لا ی)۲ + (لا ی)۲ + ۲(لا ی)(لا۲ + لا ی)\n= {(لا۲ + لا ی) + لا ی}۲\n= (لا۲ + لای + ی۲)۲","chars":956,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00207.jpg","first_page":1,"last_page":309,"title":"Kitāb-i jabr va muqābalah ‏كتاب جبر و مقابله Silsilah-ʼi Mūʼallifāt-i Madrasah-i Mubārakah-i Ḥabībīyah-ʼi Dār al-Salṭanah-ʼi Kābul","permalink":"https://afghanpress.org/book/adl0258/207","canvas":"https://afghanpress.org/iiif/adl0258/canvas/207","source":"https://afghanistandl.nyu.edu/books/adl0258/","source_pdf":"https://afghanistandl.nyu.edu/pdf/adl0258_download.pdf","rights":{"image":{"statement":"Public domain. NYU states: \"All works presented on this website are, unless otherwise indicated, in the public domain. The images available on this website may be freely reproduced, distributed and transmitted by anyone for any purpose, commercial or non-commercial.\"","uri":"http://rightsstatements.org/vocab/NoC-US/1.0/","holder":"New York University Libraries","source":"https://afghanistandl.nyu.edu/about.html","delivery":"Images are served from a copy mirrored by this project, not from NYU's servers, under the reproduction terms above.","endorsement":"This is an independent project. It is not affiliated with, endorsed by, or reviewed by New York University."},"text":{"statement":"Machine-generated transcription, dedicated to the public domain under CC0 1.0. No warranty of accuracy: see the provenance block on every page.","uri":"https://creativecommons.org/publicdomain/zero/1.0/","holder":"Steps Ventures"}},"provenance":{"text_produced_by":"gemini-3.1-pro-preview","thinking_level":"low","read_completed":"2026-08-09","per_page_confidence":null,"per_page_confidence_note":"Not recorded during the corpus run. No calibrated per-page score exists, and none is estimated here.","human_reviewed":false,"accuracy_context":"Roughly two thirds of characters agree with a modern printed edition of the same text. Much of the disagreement is editorial, not misreading. Treat the transcription as a finding aid and read the page image before quoting.","primary_source":"The page image. The text is an index into it."}}