1. Applications of Expansion and Factorisation SLIDESHOW 17 MATHEMATICS MR SASAKI ROOM 307

2. Objectives Use the difference of two squares to make certain numerical calculations Use the difference of two squares to make certain numerical calculations Be able to prove certain simple numerical facts Be able to prove certain simple numerical facts

3. The Difference of Two Squares What is the difference of two squares? This rule has many uses to help make calculations easier.

4. The Difference of Two Squares Let’s use this identity to help us make some numerical calculations. Example

5. The Difference of Two Squares We also need to consider the opposite principle. Example

6. Answers

7. Numerical Proofs Before we look at proofs, we should recall some vocabulary. Odd - Even - Consecutive Integers -

8. Proofs (Format) When you prove something, there should be three steps: Step 1 - Step 2 - Perform the necessary calculation. Write what you need to in the correct form. Step 3 - State that as it’s now in the correct form, the proof for the original expression is now complete.

9. Numerical Proofs Let’s try a simple proof and divide the steps up. Example Prove that an odd number squared is odd. Step 1 Step 2 Step 3

10. Numerical Proofs Let’s try another. Example If two integers are odd, their sum is even. Step 1 Step 2 Step 3

11. Answers – Easy (Top)

12. Answers – Easy (Bottom)

13. Answers – Hard (Top)

14. Answers – Hard (Bottom)