Factorising
- 1. Starter Expand: 1. 3𝑔 𝑔 + 4 2. 𝑥2 𝑥 + 2 3. 𝑥2 𝑥 − 1 4. 2𝑎 3 + 𝑎 − 2(4𝑎 − 2) 5. ( 𝑥 + 3) ( 𝑥 – 3) Find the common factors: 1. 12 and 20 2. 24 and 56 3. 4a and 12 4. 25𝑎2 and 15𝑎3
- 2. Starter Expand: 1. 3𝑔2 + 12𝑔 2. 𝑥3 + 2𝑥2 3. 𝑥3 − 𝑥2 4. 2𝑎2 − 2𝑎 − 4 Find the common factors: 1. 4 2. 8 3. 4 4. 5𝑎2
- 3. Factorising Expressions Thursday 5th November Objectives:To be able to Factorise Expressions
- 4. Factorising – What does it mean? 2 𝑦 + 3 = 2𝑦 + 6 Expanding Factorising – Reverse of expanding
- 5. Factorising – What does it mean? 2 𝑦 + 3 = 2𝑦 + 6 Expanding Factorising Factorising – Put in the brackets!
- 6. Factorising – How do we do it? 2𝑦2 + 6𝑦 Look for the highest common factor "2𝑦" 2𝑦(𝑦 + 3) Take out the common factors and put in the brackets Check the answer by expanding it back out again.
- 7. Factorise Factorise: 12𝑥2 𝑦 + 6𝑥𝑦2 “3𝑥𝑦(4𝑥 + 2y)”
- 8. Factorise Factorise: 12𝑥2 𝑦 + 6𝑥𝑦2 “3𝑥𝑦(4𝑥 + 2y)” Is this wrong?
- 9. Factorise Factorise: 12𝑥2 𝑦 + 6𝑥𝑦2 “6𝑥𝑦(2𝑥 + 𝑦)Is this wrong?
- 10. Factorise – Part 1 Factorise: 12𝑥2 𝑦 + 6𝑥𝑦2 “3𝑥𝑦(4𝑥 + 2y)” “6𝑥𝑦(2𝑥2 + 𝑦2)" Both are correct, why is it different? Factorised fully Get used to doing this
- 11. Look at these What do you see? Factorise completely : 3𝑎2 𝑏5 𝑐 + 27𝑎𝑏𝑐 9𝑎𝑏𝑐(𝑎𝑏4 + 9) 𝑎𝑏𝑐(3𝑎𝑏4 + 27) 3𝑎𝑏𝑐(𝑎𝑏4 + 9)
- 12. Look at these What do you see? Factorise completely : 3𝑎2 𝑏5 𝑐 + 27𝑎𝑏𝑐 9𝑎𝑏𝑐(𝑎𝑏4 + 9) 𝑎𝑏𝑐(3𝑎𝑏4 + 27) 3𝑎𝑏𝑐(𝑎𝑏4 + 9) Changed the numbers to common multiples Not Fully Factorised Correct answer
- 13. Exercise – Let’s get through this quick! 1. 2x + 10 2. 15 − 3m 3. 28 − 56n 4. 𝑥2 + 2𝑥 5. 3𝑥2 − 9𝑥 6. 𝑥3 − 𝑥2 1. 12𝑦2 + 8𝑦 2. 2𝑎2 − 𝑎 3. −7𝑥 − 8 4. ℎ2 − 25h Extension: 1. ℎ2 − 25 2. 𝑥2 − 16 You have 10 minutes…
- 14. Exercise – Let’s get through this quick! 1. 2(x + 5) 2. 3 5 − 𝑚 3. 28 1 − 2𝑛 4. 𝑥(𝑥 + 2) 5. 3𝑥 𝑥 − 3 6. 𝑥2(𝑥 − 1) 1. 4𝑦(3𝑦 + 2) 2. 𝑎 2𝑎 − 1 3. −1 7𝑥 + 8 4. ℎ ℎ − 25 Extension: 1. ℎ + 5 ℎ − 5 2. (𝑥 + 3)(𝑥 − 3)
- 15. Factorise – Part 2 Factorise Completely: 𝑥2+2𝑥 − 15 𝑥 + 5 × (𝑥 − 3) × ( ) 𝑥 × (𝑥 ) 𝑥 + × (𝑥− ) Multiply to get -15 -3 and 5 3 and -5 -1 and 15 1 and -15 Add to make 2 -3 and 5 3 and -5 -1 and 15 1 and 15
- 16. Factorise – Part 2 Factorise Completely: 𝑥2−7𝑥 + 6 𝑥 − 1 × ( 𝑥 − 6 ) × ( ) 𝑥 × (𝑥 ) 𝑥 − × (𝑥− ) Multiply to get 6 1 and 6 -1 and -6 2 and 3 -2 and -3 Add to make -7 1 and 6 -1 and -6 2 and 3 -2 and -3
- 17. Exam Questions Factorise: 8𝑥3 𝑦2 − 4𝑥𝑦3 = 4𝑥2 𝑦2(2𝑥 − 𝑦) Factorise: 2𝑧2 + 𝑧 = 𝑧(2𝑧2 + 1)