Algebra 1

I know the answers, I just don't know how to solve it and show my work.

1. (3√6 + 5√10)^2 - 286 + 60√15

2. (2 + √10)(2 - √10) - -6

3. y = √6x-18 - x (greater then or equal to) 3

Thank you

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  1. I assume you want to simplify the first two

    1. (3√6 + 5√10)^2 - 286 + 60√15
    You must know how to square a binomial ...
    = 54 + 30√60 + 250 - 286 + 60√15
    = 18 + 60√15 + 60√15
    = 18 + 120√15

    2. the first part is the expansion of a difference of squares pattern, you must know that

    3. y = √6x-18 - x
    what about it?

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  2. Fail. It wrote it wrong. These are the problems:

    (3√6 + 5√10)^2

    y = √6x-18

    I solved the second one.
    Here are my answers, I just need to know how to solve:

    286 + 60√15

    x (greater than or equal to) 3

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  3. Of course, if you knew how to solve them, you would naturally know how to show your work ...

    #1 As always, (a+b)^2 = a^2+2ab+b^2

    (3?6 + 5?10)^2
    = (3?6)^2 + 2(3?6)(5?10) + (5?10)^2
    = 54 + 30?60 + 250
    = 304 + 60?15

    So,

    (3?6 + 5?10)^2 - 286 + 60?15
    = 304+60?15 - 286 + 60?15
    = 18 + 120?15

    #2 As always, (a+b)(a-b) = a^2-b^2

    (2 + ?10)(2 - ?10) - -6
    = 2^2 - (?10)^2 + 6
    = 4 - 10 + 6
    = 0

    #3
    y = ?(6x-18)
    y = ?6 ?(x-3)
    This is just the graph of y=?x
    shifted right 3 and stretched vertically by a factor of ?6

    http://www.wolframalpha.com/input/?i=%E2%88%9A(6x-18)

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  4. 1.

    ( a + b ) ^ 2 = a ^ 2 + 2 a * b + b ^ 2

    so

    ( 3 √6 + 5 √10 ) ^ 2 = ( 3 √6 ) ^ 2 + 2 * 3 √6 * 5 √10 + ( 5 √10 ) ^ 2

    ( 3 √6 + 5 √10 ) ^ 2 - 286 + 60 √15 =

    ( 3 √6 ) ^ 2 + 2 * 3 √6 * 5 √10 + ( 5 √10 ) ^ 2 - 286 + 60 √15 =

    3 ^ 2 * 6 + 6 * √6 * 5 √10 + 5 ^ 2 * 10 - 286 + 60 √15 =

    9 * 6 + 30 * √6 * √10 + 25 * 10 - 286 + 60 √15 =

    54 + 30 * √ ( 6 * 10 ) + 250 - 286 + 60 √15 =

    18 + 30 * √60 + 60 √15 =

    18 + 30 * √( 4 * 15 ) + 60 √15 =

    18 + 30 * √ 4 * √15 + 60 √15 =

    18 + 30 * 2 * √15 + 60 √15 =

    18 + 60 √15 + 60 √15 =

    18 + 120 √15 =

    6 * 3 + 6 * 20 √15 =

    6 ( 3 + 20 √15 )

    2.

    ( 2 + √10 ) ( 2 - √10 ) - -6 =

    ( 2 + √10 ) ( 2 - √10 ) + 6

    ( a + b ) ( a - b ) = a ^ 2 - b ^ 2

    in this case:

    ( 2 + √10 ) ( 2 - √10 ) = 2 ^ 2 - ( √10 ) ^ 2 = 4 - 10 = - 6

    So:

    ( 2 + √10 ) ( 2 - √10 ) - -6 =

    ( 2 + √10 ) ( 2 - √10 ) + 6 =

    - 6 + 6 = 0

    3.

    y = √6x-18 - x (greater then or equal to) 3 doesn't make sense.

    But:

    √ 6 x -18 - x ≥ 3 Add 18 to both sides

    √ 6 x -18 - x + 18 ≥ 3 + 18

    √6 x - x ≥ 21

    x ( √6 - 1 ) ≥ 21 Divide both sides by ( √6 - 1 )

    x = 21 / ( √6 - 1 )

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  5. As you can see from the responses here, if you want a good answer, you need to be clear on just what it is you are asking.

    It is not our job to figure out what you mean -- it is your job to say it so clearly that you cannot be misunderstood!

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