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anonymous

  • one year ago

Part A: The area of a square is (9x2 − 12x + 4) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points) Part B: The area of a rectangle is (25x2 − 16y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

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  1. anonymous
    • one year ago
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    @Keigh2015

  2. anonymous
    • one year ago
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    @Kash_TheSmartGuy

  3. anonymous
    • one year ago
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    @phi

  4. anonymous
    • one year ago
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    Can someone help me

  5. anonymous
    • one year ago
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    hi

  6. mathstudent55
    • one year ago
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    Part A. Factor 9x2 − 12x + 4 This trinomial follows the pattern \(a^2 - 2ab + b^2 = (a - b)^2\)

  7. anonymous
    • one year ago
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    ok im gonna plug it in

  8. anonymous
    • one year ago
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    one sec

  9. mathstudent55
    • one year ago
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    To factor it, first, what is it whose square is to 9x^2?

  10. anonymous
    • one year ago
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    um..

  11. anonymous
    • one year ago
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    idk

  12. mathstudent55
    • one year ago
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    What do you square to get 9x^2? ___ * ___ = 9x^2 What is the square root of 9?

  13. mathstudent55
    • one year ago
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    What number times itself equals 9?

  14. anonymous
    • one year ago
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    3

  15. mathstudent55
    • one year ago
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    Good. What times itself is x^2?

  16. anonymous
    • one year ago
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    1

  17. anonymous
    • one year ago
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    wait no

  18. anonymous
    • one year ago
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    nothing

  19. mathstudent55
    • one year ago
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    No. 1 * 1 = 1 The answer is x. x * x = x^2 Ok?

  20. anonymous
    • one year ago
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    okay

  21. mathstudent55
    • one year ago
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    That means (3x)(3x) = 9x^2 The square root of 9x^2 is 3x

  22. anonymous
    • one year ago
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    ok

  23. mathstudent55
    • one year ago
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    Now we deal with the 4. What is the square root of 4?

  24. anonymous
    • one year ago
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    2

  25. mathstudent55
    • one year ago
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    Good. Since we have the pattern: \(a^2 - 2ab + b^2 = (a - b)^2\) in this case we have: \(9x^2 - 12x + 4 = (3x - 2)^2\)

  26. mathstudent55
    • one year ago
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    That means the side of the square is 3x - 2 units

  27. anonymous
    • one year ago
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    so thats the length of each side?

  28. anonymous
    • one year ago
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    @phi

  29. mathstudent55
    • one year ago
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    Yes. Since it's a square, all sides measure 3x - 2

  30. anonymous
    • one year ago
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    ooh okay thankyou

  31. anonymous
    • one year ago
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    can you help with B?

  32. mathstudent55
    • one year ago
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    In part B, you have a rectangle. A rectangle may or may not be a square. We need to factor (25x2 − 16y2)

  33. anonymous
    • one year ago
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    (5x+4y)(5x−4y)

  34. mathstudent55
    • one year ago
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    Here, the pattern of the binomial is: \(a^2 - b^2 = (a + b)(a - b) \) This is called the difference of two squares.

  35. mathstudent55
    • one year ago
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    You are correct. As you can see the sides are not equal, so this rectangle is not a square.

  36. mathstudent55
    • one year ago
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    Two opposite sides have length 5x + 4y, and the other two opposite sides have length 5x - 4y

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