Productos notables y factorización paso a paso: cuadrado de binomio y diferencia de cuadrados

Is (x+4)² x²+16? 🚫 That's THE mistake that costs you points. In this video, you'll learn special products as shortcuts and how to factor with confidence, understanding WHY they work (not just memorizing them blindly). What you'll learn ✅ • Square of a binomial: (a+b)² = a² + 2ab + b² — and why you CAN'T forget the double product. • Sum and difference of squares: (a+b)(a−b) = a² − b² — why the middle term disappears. • Factoring by taking out the common factor: 5x + 15 = 5(x+3). • Difference of squares: x² − 81 = (x+9)(x−9) — the sum and difference of squares read backwards. • A mental math trick: 21² = (20+1)² = 441, without a calculator. The mistake we corrected ❌➡️✅ (x+4)² is NOT x²+16. The double product is missing: (x+4)² = x² + 8x + 16. Challenge 🧠 Expand (x−7)² and leave your result in the comments (pay attention to the sign of the middle term). 📄 Materials for this lesson (free PDF) ✍️ Practice activity: https://da.gd/POvYkK ✅ Answer key (check your answers): https://da.gd/Vgj7 📘 Study guide: https://da.gd/HbKfdt Community 💬 Did you get stuck on any of them? Write it in the comments and I'll answer you. Subscribe so you don't miss the next one. 📌 Chapters 0:00 The error (x+4)² and what we'll see 0:29 What is a special product and what is factoring 0:55 Square of a binomial (a+b)² 1:53 Sum and difference of squares (a+b)(a−b) 2:51 Factoring: common factor 3:36 Difference of squares 4:16 What it's for: mental calculation (21²) 4:54 Challenge: (x−7)² 5:35 Review and challenge — 📚 Level: 9th Grade · Mathematics — Algebra and functions (special products and factoring). 🎯 PAES 2027: Content of Mathematical Competency M1 (Algebra and functions axis). Foundation for equations, functions, and simplification. 📖 Sources: MINEDUC Curriculum Framework, 1st Year High School Mathematics, Learning Objective 03. #mathematics #specialproducts #factorization #algebra #squareofbinomial #differenceofsquares #PAES #PAES2027 #1styearhighschoolmathematics #teachersergioseguel