Download 9th Class Math Exercise 4.7 Notes PDF – Factorize by Completing the Square (FBISE 2025)
Exercise 4.7 is the bridge between simple factorization tricks and the full power of quadratic formulas you’ll meet in Class 10. Here you practice completing the square—a technique that rewrites any quadratic as a perfect square plus (or minus) a constant. Why does this matter? First, it lets you jump straight to vertex form when graphing parabolas, shaving minutes off MCQ sections. Second, it is the fast lane to deriving the quadratic formula instead of memorizing it. Finally, examiners at FBISE and BISE Faisalabad often embed a “square‑complete” step inside multi‑part questions; mastering it now prevents mid‑solution panic. This PDF begins with a two‑page visual overview that compares expansion, completing the square and the product‑sum method you used in Exercise 4.2. You’ll see exactly when each path is quickest. The guide then walks through eight worked examples, carefully annotating every coefficient change so you never lose track of that crucial half‑coefficient (b/2)2 term. After the examples, a “Common Pitfalls” list highlights easy‑to‑miss sign errors and reminds you to check for common factors before starting. Need a confidence boost? Our board‑style practice set mirrors the mark distribution in recent FBISE and Faisalabad board papers—so you’ll know precisely how many steps examiners expect. Each question is paired with a one‑line rubric so you can self‑mark and spot where you lose marks.
More Notes for Chapter 4 – Factorization & Algebraic Manipulation
Exercise 4.5 Notes
Exercise 4.6 Notes
Exercise 4.8 Notes
Misc Exercise 4 Notes
Want a clean, printable booklet that strings all Unit 4 exercises together? Request this PDF through our download page—perfect for offline revision.
