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- 1. Image Source: http://www.strangezoo.com
- 2. Expanding Two Brackets is a skill needed for Graphing and Analysing“Parabola” shapes, such as the Sydney Harbour Bridge.Eg. It is a very basic and very important skill used in doing other partsof mathematics, like dribbling is a fundamental skill of Basketball.y = -0.00188(x – 251.5)(x – 251.5) + 118
- 3. The previous two brackets equation was created from measurementstaken off a photo of the Bridge, where pixels were converted to meters.
- 4. Expanding and simplifying the Two Brackets Equation, gives us anAlgebra equation we can graph using an online graphing application.
- 5. For the numeric expression below, thereare two ways we can get to the answer:(2 + 3) (4 + 5) = 451) Using “BODMAS” or “Pemdas”2) Using the “Binomial Expansionor “FOIL” or “Crab Claws” method.
- 6. When we apply “BODMAS” or “Pemdasto the expression below, we need to do theAdding in the “Brackets” (or “Parenthesis”),before we do the “Multiplying”.(2 + 3) (4 + 5) = (2 + 3) x (4 + 5)= 5 x 9= 45
- 7. We use a set MULTIPLYING PATTERN(2 + 3) (4 + 5) =2 x 4 + 2 x 5 + 3 x 4 + 3 x 5= 8 + 10 + 12 + 15= 45Image Source: http://www.ceramicmosaicart.com
- 8. Image Source: http://www.ceramicmosaicart.comTo help remember the Pattern, think of the items in the firstbracket as two Crab Claws, which each reach into the secondbracket and grab the values there and multiply them.
- 9. 2(n + 5) = 2xn + 2x5 = 2n + 10We cannot do Algebra expressions withBODMAS, because n+3 does notsimplify to a whole number.So we have to use Distributive Rule.The “Crab Claws” is simply two lots of theDistributive Rule one after each other.
- 10. Expand the Binomial: (h + 3) (y + 5)(h + 3) (y + 5) =h x y + h x 5 + 3 x y + 3 x 5= hy + 5h + 3y + 15Image Source: http://www.ceramicmosaicart.com
- 11. Expand the Binomial: (k + 2) (v - 1)(k + 2) (v - 1) =k x v + k x -1 + 2 x v + 2 x -1= kv + -1k + 2v + -2= kv - k + 2v - 2Use Integer Rulesto Simplify each+ - to just be a -
- 12. Expand the Binomial: (m - 2) (n - 6)(m - 2) (n - 6) =m x n + m x -6 + -2 x n + -2 x -6= mn + -6m + -2n + 12= mn - 6m - 2n + 12Use Integer Rulesto Simplify each+ - to just be a -
- 13. Expand the Binomial: (5a + h) (y + 2k)(5a + h) (y + 2k) =5a x y + 5a x 2k + h x y + h x 2k= 5ay + 10ak + hy + 2hk
- 14. The examples we have done so far all had FOUR PART ANSWERS.This is because the brackets had four different items in them:(a + b) (c + d) = ac + ad + bc + bdWhen we have brackets with some “Like Terms” in them,we only get THREE PART or TWO PART answers.(a + 3) (a + 2) = a2+ 3a + 2a + 6 = a2+ 5a + 6(a + 4) (a - 4) = a2+ -4a + 4a - 16 = a2- 16The following Examples show Three part and Two part Answers.vv
- 15. Expand the Binomial: (m + 4) (m + 1)(m + 4) (m + 1) =m x m + m x 1 + 4 x m + 4 x 1= m2+ m + 4m + 4= m2+ 5m + 4Simplify by Combiningthe Like Term items.
- 16. Expand the Binomial: (b - 3) (b - 2)(b - 3) (b - 2) =b x b + b x -2 + -3 x b + -3 x -2= b2– 2b – 3b + 6= b2- 5b + 6Simplify by Combiningthe Like Term items.
- 17. Expand the Binomial: (h - 7) (h + 8)(h - 7) (h + 8) =h x h + h x 8 + -7 x h + -7 x 8= h2+ 8h – 7h + -56= h2+ h - 56Simplify by Combiningthe Like Terms .
- 18. Expand the Binomial: (k + 2) (k - 2)(k + 2) (k - 2) =k x k + k x -2 + 2 x k + 2 x -2= k2– 2k + 2k + -4= k2- 4Simplify by Combiningthe Like Terms to ZERO.
- 19. Expand the Binomial: (3m + 2) (2m + 1)(3m + 2) (2m + 1) =3m x 2m + 3m x 1 + 2 x 2m + 2 x 1= 6m2+ 3m + 4m + 2= 6m2+ 7m + 2Simplify by Combiningthe Like Terms .
- 20. Expand the Binomial: (a - 2)2(a - 2)2= (a - 2) (a - 2) =a x a + a x -2 + -2 x a + -2 x -2= a2– 2a – 2a + 4= a2– 4a + 4Simplify by Combiningthe Like Terms .
- 21. http://passyworldofmathematics.comVisit our site for Free Mathematics PowerPoints

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