# 1.2 - EXERCISES 1.2, page 22 1. 2. 3. 4. 5. (7x2 - 2x + 5)...

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EXERCISES 1.2, page 22 1. (7 x 2 - 2 x + 5) + (2 x 2 + 5 x - 4) = 7 x 2 - 2 x + 5 + 2 x 2 + 5 x - 4 = 9 x 2 + 3 x + 1. 2. (3 x 2 + 5 xy + 2 y ) + (4 - 3 xy - 2 x 2 ) = 3 x 2 + 5 xy + 2 y + 4 - 3 xy - 2 x 2 = x 2 + 2 xy + 2 y + 4. 3. (5 y 2 - 2 y + 1) - ( y 2 - 3 y - 7) = 5 y 2 - 2 y + 1 - y 2 + 3 y + 7 = 4 y 2 + y + 8. 4. 3(2 a - b ) - 4( b - 2 a ) = 6 a - 3 b - 4 b + 8 a = 14 a - 7 b = 7(2 a - b ). 5. x - {2 x - [- x - (1 - x )]} = x - {2 x - [- x - 1 + x ]} = x - {2 x + 1} = x - 2 x - 1 = - x - 1. 6. 3 x 2 - { x 2 + 1 - x [ x - (2 x - 1)]} + 2 = 3 x 2 - { x 2 + 1 - x [ x - 2 x + 1]} + 2 = 3 x 2 - { x 2 + 1 - x [- x + 1]} + 2 = 3 x 2 - { x 2 + 1 + x 2 - x } + 2 = 3 x 2 - {2 x 2 - x + 1} + 2 = x 2 - 1 + x + 2 = x 2 + x + 1. 7. () ( ) 1 3 1 1 3 1 1 3 1 1 3 1 1 1 −+ −− −+ = −++ +− eee e 2 21 3 2 . 33 ee e 3 + =+−= 8. −+++−= −+−++− 3 4 1 4 100 1 2 1 4 120 3 4 1 4 1 4 1 2 100 120 yx xy yyxx =− + 1 2 1 4 20 . 9. 38 8 2 1 2 3 4 342 8 1 2 11 4 +− + = ⋅++ yxy x y =+ + − 62 8 1 2 11 4 . 1 Preliminaries 12

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10. 22 8 2 16 16 933 3 8 6 48 48 18 18 9 xxx x x xxx xx ++ − −+ − − + = 2 2 8 6 48 48 18 18 56 60 18 99 2(28 30 9) . 9 x x xx − + == −+ = 11. ( x + 8)( x - 2) = x ( x - 2) + 8( x - 2) = x 2 - 2 x + 8 x - 16 = x 2 + 6 x - 16. 12. (5 x + 2)(3 x - 4) = 5 x (3 x - 4) + 2(3 x - 4) = 15 x 2 - 20 x + 6 x - 8 = 15 x 2 - 14 x - 8. 13. ( a + 5) 2 = ( a + 5)( a + 5) = a ( a + 5) + 5( a + 5) = a 2 + 5 a + 5 a + 25 = a 2 + 10 a + 25. 14. (3 a - 4 b ) 2 = (3 a - 4 b )(3 a - 4 b ) = 3 a (3 a - 4 b ) - 4 b (3 a - 4 b ) = 9 a 2 - 12 ab - 12 ab + 16 b 2 = 9 a 2 - 24 ab + 16 b 2 . 15. ( x + 2 y ) 2 = ( x + 2 y )( x + 2 y ) = x ( x + 2 y ) + 2 y ( x + 2 y ) = x 2 + 2 xy + 2 yx + 4 y 2 = x 2 + 4 xy + 4 y 2 . 16. (6 - 3 x ) 2 = (6 - 3 x )(6 - 3 x ) = 6(6 - 3 x ) - 3 x (6 - 3 x ) = 36 - 18 x - 18 x + 9 x 2 = 36 - 36 x + 9 x 2 . 17. (2 x + y )(2 x - y ) = 2 x (2 x - y ) + y (2 x - y ) = 4 x 2 - 2 xy + 2 xy - y 2 = 4 x 2 - y 2 . 18. (3 x + 2)(2 - 3 x ) = 3 x (2 - 3 x ) + 2(2 - 3 x ) = 6 x - 9 x 2 + 4 - 6 x = -9 x 2 + 4. 19. ( x 2 - 1)(2 x ) - x 2 (2 x ) = 2 x 3 - 2 x - 2 x 3 = -2 x . 20. ( ) () [ ( // / xxx 12 1 2 1 2 1 2 11 1 +− −= + −− ) ] 1 1 Preliminaries 13
== = 1 2 12 2 11 x x x / / () . 21. 22 2 2 tt t tt t +−= + +− di 2 =+ + =+ +− =+ = + 2 24 42 2 2 t t t t t t t 1 . 22. 2 x 2 + (- x + 1) 2 = 2 x 2 + (- x + 1)(- x + 1) = 2 x 2 + x 2 - 2 x + 1 = 3 x 2 - 2 x + 1. 23. 4 x 5 - 12 x 4 - 6 x 3 = 2 x 3 (2 x 2 - 6 x - 3). 24. 4 x 2 y 2 z - 2 x 5 y 2 + 6 x 3 y 2 z 2 = 2 x 2 y 2 (2 z - x 3 + 3 xz 2 ). 25. 7 a 4 - 42 a 2 b 2 + 49 a 3 b = 7 a 2 ( a 2 - 6 b 2 + 7 ab ). 26. 3 x 2/3 - 2 x 1/3 = x 1/3 (3 x 1/3 - 2). 27. e - x - xe - x = e - x (1 - x ). 28. 2 ye xy ² + 2 xy 3 e xy ² = 2 ye xy ² (1 + xy 2 ). 29. 3 x . 52 3 2 32 1 2 xxx −− − −= // / 30.

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## 1.2 - EXERCISES 1.2, page 22 1. 2. 3. 4. 5. (7x2 - 2x + 5)...

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