{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1.2 - EXERCISES 1.2 page 22 1 2 3 4 5(7x2 2x 5(2x2 5x 4 =...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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 + − − + = + + + e e e e 2 2 1 3 2 . 3 3 e e e e e 3 + = + = 8. + + + = − + + + 3 4 1 4 100 1 2 1 4 120 3 4 1 4 1 4 1 2 100 120 y x x y y y x x = − + 1 2 1 4 20 y x . 9. 3 8 8 2 1 2 3 4 3 4 2 8 1 2 11 4 + + = + + y x y x y = + + 6 2 8 1 2 11 4 x y . 1 Preliminaries 12
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
10. 2 2 2 2 8 2 16 16 2 2 9 3 3 3 8 6 48 48 18 18 9 x x x x x x x x x x + + + + + + = 2 2 2 2 8 6 48 48 18 18 56 60 18 9 9 2(28 30 9) . 9 x x x x x x x x x + + + + = = + = 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. ( )( ) ( )( ) [( ) ( / / / / / / / x x x x x x x 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 1 + = + )] 1 1 Preliminaries 13
Image of page 2
= = = 1 2 1 2 1 2 2 1 1 x x x / / ( ) . 21. 2 2 2 2 2 2 t t t t t t t t + = + + d i ( )( ) 2 = + + = + + = + = + 2 2 2 2 4 2 2 4 2 2 2 2 2 2 2 ( ) ( ) t t t t t t t t 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. 2 4 3 x .
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern