SOLUTION: Expand (what does expand mean in relation to the below problem?) {{{ (x^2y^-2/z^2)(z^2/y^2(2x^-2)^-1-4x^2y^0/z^-2) }}}

Algebra ->  Equations -> SOLUTION: Expand (what does expand mean in relation to the below problem?) {{{ (x^2y^-2/z^2)(z^2/y^2(2x^-2)^-1-4x^2y^0/z^-2) }}}       Log On


   

Question 171085: Expand (what does expand mean in relation to the below problem?)
+%28x%5E2y%5E-2%2Fz%5E2%29%28z%5E2%2Fy%5E2%282x%5E-2%29%5E-1-4x%5E2y%5E0%2Fz%5E-2%29+

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Expand (what does expand mean in relation to the below problem?)
+%28x%5E2y%5E-2%2Fz%5E2%29%28z%5E2%2Fy%5E2%282x%5E-2%29%5E-1-4x%5E2y%5E0%2Fz%5E-2%29+
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=%28x%5E2y%5E-2%2Fz%5E2%29%28z%5E2%2Fy%5E2%282x%5E-2%29%5E-1-4x%5E2z%5E2%29 y^0 = 1, and 1/z^-2 = z^2
=%28x%5E2y%5E-2%29%281%2Fy%5E2%282x%5E-2%29%5E-1-4x%5E2%29 z^2 cancels
=%28x%5E2y%5E-2%29%281%2Fy%5E2%28x%5E2%2F2%29-4x%5E2%29 (2x^-2)^-1 = x^2/2
=%28x%5E2y%5E-2%29%282%2Fy%5E2%28x%5E2%29-4x%5E2%29
=%28x%5E2%2Fy%5E2%29%2A%282%2Fy%5E2%28x%5E2%29%29+-+%28x%5E2%2Fy%5E2%29%2A%284x%5E2%29
=%281%2Fy%5E2%29%2A%282%2Fy%5E2%29+-+4%28x%5E4%2Fy%5E2%29
=%282%2Fy%5E4%29+-+4%28x%5E4%2Fy%5E2%29
=%282%2Fy%5E4%29+-+4x%5E4y%5E2%2Fy%5E4
=%282+-+4x%5E4y%5E2%29%2Fy%5E4
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Expand is multiplying terms, usually binomials or larger. This problem was mostly simplification, tho, combining terms.