LLG
Advanced Math and Science Pilot Class
Mathematics, Grade 10
2014 – 2015 .
Paris – Abu Dhabi
NAME : ……………………………………………………….
Chapter 5 : Discovering the special products
In an Excel sheet, copy down the following table, entering the adequate formula so that 𝑎 and 𝑏 are random integers
comprised between 1 and 10.
1. Is (𝑎 + 𝑏)2 equal to 𝑎2 + 𝑏 2 ?
2. How much is the difference between the two ? Use your Excel table to answer.
(𝑎 + 𝑏)2 − (𝑎2 + 𝑏 2 ) = …………………………………………..……………………….
3. Can you then conjecture a formula for this expression ?
(𝑎 + 𝑏)2 = ………………………………………….
4. Check it out expanding (𝑎 + 𝑏)2 :
(𝑎 + 𝑏)2 = (𝑎 + 𝑏)(𝑎 + 𝑏) =…………………………………………..……………………….
2
5. We are now interested in (𝑎 − 𝑏)2 . Writing it (𝑎 + (−𝑏)) and using the previous formula, give the
expanded form of (𝑎 − 𝑏)2 = …………………………………………..……………………….
6. Finally, expand the following expression to find the third special product :
(𝑎 + 𝑏)(𝑎 − 𝑏) =…………………………………………..……………………….