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  # Expanding two brackets
  
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  ### Transcript
  
  • 1. Objective Be able to expand brackets and simplify the expressions that arise
  • 2. Question (Level 6) &#x2022; Expand and simplify the following expression (2a + 3)(4a + 2)
  • 3. Step 1 (2a + 3)(4a + 2) 2a +3 4a +2 Multiply the individuals components together
  • 4. 2a +3 4a 8a2 +2
  • 5. 2a +3 4a 8a2 +12a +2
  • 6. 2a +3 4a 8a2 +12a +2 +4a
  • 7. 2a +3 4a 8a2 +12a +2 +4a +6
  • 8. Step 2 &#x2022; Now collect the like terms 2a +3 4a 8a2 +12a +2 +4a +6 16a
  • 9. Step 3 So we have 2a +3 4a 8a2 +12a +2 +4a +6 8a2 + 16a + 6
  • 10. This will always work! You may have to deal with negatives too, but don&#x2019;t worry it&#x2019;s just as easy.
  • 11. Dealing with negatives Expand and simplify the following expression (3b + 2)(4b &#x2013; 6)
  • 12. Step 1 (3b + 2)(4b &#x2013; 6) 3b +2 4b -6 Multiply the individuals components together
  • 13. 3b +2 4b 12b2 -6
  • 14. 3b +2 4b 12b2 +8b -6
  • 15. 3b +2 4b 12b2 +8b -6 -18b
  • 16. 3b +2 4b 12b2 +8b -6 -18b -12
  • 17. Step 2 &#x2022; Now collect the like terms 2a +3 4a 12b2 +8b +2 -18b -12 -10b
  • 18. Step 3 So we have 2a +3 4a 12b2 +8b +2 -18b -12 12b2 &#x2013;10b &#x2013; 12
  • 19. That&#x2019;s it! Just be careful when you are multiplying negative numbers and take your time when collecting like terms.
  • 20. Let&#x2019;s try some questions &#x2013; You only have five minutes! &#x2022; Expand and simplify: 1) (2a + 7)(6a + 2) 2) (4b + 5)(3b +9) 3) (5c + 4)(8c &#x2013; 2) 4) (7d + 5)(3d &#x2013; 4) 5) (9y &#x2013;2)(3y + 6) 6) (4p &#x2013; 3)(2p &#x2013; 6) 7) (8m &#x2013; 2)(7m &#x2013; 4)
  • 21. Time is up! Let&#x2019;s check some answers
  • 22. Did you get them correct? 1) (2a + 7)(6a + 2) 2) (4b + 5)(3b +4) 3) (5c + 4)(8c &#x2013; 2) 4) (7d + 5)(3d &#x2013; 4) 5) (9y &#x2013;2)(3y + 4) 6) (4p &#x2013; 3)(2p &#x2013; 6) 7) (8m &#x2013; 2)(7m &#x2013; 4) 12a2 + 46a +14 12b2 + 31b +20 40c2 +22c - 8 21d2 &#x2013; 13d -20 27y2 +30y - 8 8p2 &#x2013;30p + 18 56m2 &#x2013; 46m +8
  • 23. THINK! Did you meet the objective of the lesson? Be able to expand brackets and simplify the expressions that arise