1. Slideshow 15 Mathematics Mr Sasaki Room 307 BRACKET EXPANSION AND FACTORISATION

2. OBJECTIVES

3. Today, we are dealing with a certain form of polynomial. Each has a special name. DEFINITIONS 4 This is a “constant”. It doesn’t change. It’s also a monomial (one term). This is “linear”. This is a “quadratic”. This is a “cubic”. This is a “quartic”. This is a “quintic”.

4. To expand a pair of brackets representing a quadratic, we multiply each term inside each bracket by each term in the other bracket. Here are the combinations. EXPANDING BRACKETS Notice that ab and cd are not combinations.

5. Try the example below. EXPANDING BRACKETS Example = + - - 6 = Try the worksheet!

6. ANSWERS

7. Placing a quadratic into a pair of brackets is called “factorisation”. This is the opposite of expanding brackets and more difficult to do. FACTORISATION Let’s try a linear expression. Example What is the largest factor that divides into 9 and 6? 3 = 3( ) The contents of the bracket is divided by the coefficient outside.

8. FACTORISATION A quadratic is more difficult. Example We need to think of two numbers which add together to make 5 and multiply to make 6. 2 and 3 = ( ) + 2 + 3 If you are unsure it’s right, expand it out to check!

9. FACTORISATION Let’s try another example. Example We need to think of two numbers which add together to make -5 and multiply to make -36. Hint: 9 – 4 is 5 and 9 x 4 is 36. -9 and 4 -9 + 4 = -5 -9 x 4 = -36 = ( )( ) - 9 + 4 Try the worksheet!

10. ANSWERS

11. SOLVING QUADRATIC EQUATIONS THROUGH FACTORISATION Example ( )( ) = 0 - 5 - 1

12. SOLVING QUADRATIC EQUATIONS THROUGH FACTORISATION Example ( )( ) = 0 + 6 + 12 Try the last worksheet!

13. ANSWERS 7