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# Expanding Binomial Brackets

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### Expanding Binomial Brackets

1. 1. Image Source: http://www.strangezoo.com
2. 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. 3. The previous two brackets equation was created from measurementstaken off a photo of the Bridge, where pixels were converted to meters.
4. 4. Expanding and simplifying the Two Brackets Equation, gives us anAlgebra equation we can graph using an online graphing application.
5. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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 .