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Math Help - Rearanging

  1. #1
    Newbie
    Joined
    Oct 2010
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    1

    Rearanging

    Hi I'm a tad vexed by this problem

    y(y+z) = a(a-z)

    I'm trying to rearange it in terms of z.

    I thought I should first multiply out the brackets

    y^2 + yz = a^2 -az (where ^2 is squared)

    Then take the y^2 away

    yz = a^2-y^2-az

    Divide by y

    z= (a^2 - y^2 - az)y

    now how do I get rid of z frm the right side or am I aproaching this wrong, another way I tried was taking the whole right side from the left to make a kind of quadratic equation.

    Thanks in advance
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  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
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    Mauritius
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    1,260
    We take it from here:

    y^2 + yz = a^2 -az

    Move all the z on one side and the rest on the other.

    yz + az = a^2 - y^2

    Factor z;

    z(y + a) = a^2 - y^2

    Divide by (y+a);

    z = \dfrac{a^2 - y^2}{y + a} = \dfrac{(a - y)(a + y)}{a + y} = a - y
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