Special Cases: The Difference of Two Squares & Missing Terms

Описание: 👉Full courses https://www.mathsadviceonyourdevice.com/

⚠️ What happens when a quadratic equation is “missing” a term?
0:00 – Review: the Area Method
0:08 – The “zero middle term” mystery
0:58 – Geometric proof: x² − 9
1:19 – Handling coefficients: 2x² − 200
1:40 – Quadratics with no constant term (single bracket)
2:20 – Practice and summary

In this lesson, we apply the Reverse Area Method to special cases that often confuse students — including the Difference of Two Squares and quadratics with no middle or no constant term.

By treating x² − 9 as a quadratic with a 0x middle term, students see that the same structural logic still applies.

Using geometry, we visually show that the area of x² − 3² is identical to a rectangle with sides (x + 3) and (x − 3)

No tricks. No memorisation. Just structure that makes sense 🧠📐

🎯 Key Takeaways for Teachers & Students

🔹 The 0x Concept
Why missing middle terms must be opposites (additive inverses) so they cancel

🔹 Difference of Two Squares
A geometric proof that
a² − b² = (a − b)(a + b)

🔹 Leading Coefficients Made Clear
Why expressions like
2x² − 200
should be simplified before factoring

🔹 Single-Bracket Factorisation
Understanding
x² + x
as a rectangle with width x

Who This Video Is For
🎯 Teachers who want students to understand factoring
📘 Students confused by “missing” terms
🚀 Anyone preparing for advanced algebra or Calculus


Access full courses, quizzes, and worksheets here:
👉 https://www.mathsadviceonyourdevice.com/

💎 Want More Like This?

🔎 Have a topic you’d like explained visually? Let me know
📅 New videos every week
💌 Contact: [email protected]

📌 Recommended Next Videos

📈 Gradient of a Parabola
   • Gradient of a parabola (Ep. 1 of 5)  

📊 Rules for Exponentials
   • 🧠 From Blocks to Binary: Three-Step Method...  

📐 Pythagoras’ Theorem (Visual Proof)
   • Pythagoras Theorem Using Other Shapes (Ep....  

What Is the Number e?
   • WHAT IS  THE NUMBER e AND WHERE DOES IT CO...  

🧡 Why I Teach This Way

Doing maths is like going to the gym 💪
You build strength by doing, a little every day.
My mission is to make maths clear, logical, and achievable — for students and teachers.

#DifferenceOfSquares #QuadraticEquations #VisualMath
#AlgebraTeaching #CalculusPrep #MathEducation
#MathsAdviceOnYourDevice #FlippedMaths #STEM