Expanding brackets with surds Getting ready for A-Level
Transcript of Expanding brackets with surds Getting ready for A-Level
![Page 1: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/1.jpg)
Getting ready for A-Level...Expanding brackets with surds
“The most important investment you can make is in yourself.”
Getting ready for A-Level Maths...
![Page 2: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/2.jpg)
a + b a + b≠a - b a - b≠
Expanding brackets with surds
Important rulesa x b a x b=
a =bab
Be careful...
12 = 1 x 1 = 1
22 = 2 x 2 = 4
32 = 3 x 3 = 9
42 = 4 x 4 = 16
52 = 5 x 5 = 25
62 = 6 x 6 = 36
72 = 7 x 7 = 49
82 = 8 x 8 = 64
92 = 9 x 9 = 81
102 = 10 x 10 = 100
112 = 11 x 11 = 121
122 = 12 x 12 = 144
132 = 13 x 13 = 169
142 = 14 x 14 = 196
152 = 15 x 15 = 225
Learn by heart...
![Page 3: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/3.jpg)
Expanding brackets with surdsQuestionWhat's the answer
√2 x √2 =
a b a x b=x
![Page 4: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/4.jpg)
Expanding brackets with surdsQuestionWhat's the answer
√7 x √7 =
a b a x b=x
![Page 5: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/5.jpg)
Expanding brackets with surdsQuestionWhat's the answer
√919 x √919 =
a b a x b=x
![Page 6: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/6.jpg)
Expanding brackets with surdsExpanding bracketsExpand and simplify
2(x + 4 )
![Page 7: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/7.jpg)
Expanding brackets with surdsExpanding bracketsExpand and simplify
(x + 2)(x + 4)
![Page 8: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/8.jpg)
Expanding brackets with surds
Evaluate without a calculator
√2(√8 + √50 )
My turn Your turnEvaluate without a calculator
√3(√12 + √27)
![Page 9: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/9.jpg)
Expanding brackets with surds
Express in the form a + b√3
(4 + √3 )(1 + 2√3 )
State the values of a and b.
My turn Your turnExpress in the form a + b√5
(2 + √5 )(3 + 4√5 )
State the values of a and b.
![Page 10: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/10.jpg)
Expanding brackets with surds
Express in the form a + b√3
(5 + 3√3)2
State the values of a and b.
My turn Your turnExpress in the form a + b√5
(7 + 2√5)2
State the values of a and b.
![Page 11: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/11.jpg)
Expanding brackets with surds
Express in the form a + b√3
(2√3 - 1)2
State the values of a and b.
My turn Your turnExpress in the form a + b√5
(3√5 - 2)2
State the values of a and b.
![Page 12: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/12.jpg)
Expanding brackets with surds
Simplify
(√7 - 1)(√7 + 1)
My turn Your turnSimplify
(√11 - 2)(√11+ 2)
![Page 13: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/13.jpg)
Expanding brackets with surds
(a - b)(a + b) = a2 - b2
Difference of two squares
(a + b)(a - b) = a2 - b2
![Page 14: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/14.jpg)
Expanding brackets with surds
Simplify
(2 + √5)(2 - √5)
My turn Your turnSimplify
(8 + √7)(8 - √7)
![Page 15: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/15.jpg)
Expanding brackets with surds
Simplify
(6 - 4√2)(6 + 4√2)
My turn Your turnSimplify
(10 - 3√5)(10 + 3√5)
![Page 16: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/16.jpg)
Expanding brackets with surdsReview Exercise
Evaluate without a calculator.√5(√20 + √45 )
Express in the form a + b√2. (5 + √2 )(6 + 3√2 )State the values of a and b.
Express in the form a + b√7. (2√7 - 3)2
State the values of a and b.
Express in the form a + b√6. (4 + 2√6)2
State the values of a and b.
1.
2.
3.
4.
Simplify (√13 - 2)(√13 + 2)
Simplify (7 + √6)(7 - √6)
Simplify (9 - 5√3)(9 + 5√3)
5.
6.
7.
![Page 17: Expanding brackets with surds Getting ready for A-Level](https://reader033.fdocuments.in/reader033/viewer/2022051603/62805af64340516e1439bb8a/html5/thumbnails/17.jpg)
Expanding brackets with surdsReview Exercise (Answers)
Evaluate without a calculator.√5(√20 + √45 )
Express in the form a + b√2. (5 + √2 )(6 + 3√2 )State the values of a and b.
Express in the form a + b√7. (2√7 - 3)2
State the values of a and b.
Express in the form a + b√6. (4 + 2√6)2
State the values of a and b.
1.
2.
3.
4.
Simplify (√13 - 2)(√13 + 2)
Simplify (7 + √6)(7 - √6)
Simplify (9 - 5√3)(9 + 5√3)
5.
6.
7.
25
36 + 21√2
40 + 16√6
37 - 12√7
9
43
6a = 36b = 21
a = 40b = 16
a = 37b = -12