Question 2 – Page 148 - Investigating Patterns - Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)

Transcript

Question 2 – Page 148 Show that (a + b) × (a – b) = a2 – b2 geometrically. Let’s look at this diagramImagine a Big Square: Imagine you start with a big square with side length 𝑎. Its area is 𝑎^2. Cut a Small Square: Now, imagine cutting out a small square of size 𝑏 from one corner. The area you have left is 𝑎^2−𝑏^2. The L-Shape: The shape you are left with looks like an "L". Cut and Move: If you cut a rectangle strip from the bottom of that "L" (the dotted part in your diagram) and move it to the side (the red part), you transform the L-shape into a simple Rectangle. The length of this new rectangle becomes (𝑎+𝑏) (because you added the side 𝑏 to the side 𝑎 ). The width of this new rectangle becomes (𝑎−𝑏) (because you cut off the side 𝑏 ). Conclusion: Since the area of the new rectangle is Length × Width, the area is ( 𝑎+𝑏)(𝑎−𝑏). Since this is made of the same paper as the original cut square, it must equal 𝑎^2−𝑏^2.