SOLUTION 1 Begin with x 3 y 3 = 4 Differentiate both sides of the equation, getting D ( x 3 y 3) = D ( 4 ) , D ( x 3) D ( y 3) = D ( 4 ) , (Remember to use the chain rule on D ( y 3) ) 3x 2 3y 2 y' = 0 , so that (Now solve for y' ) 3y 2 y' = 3x 2, and Click HERE to return to the list of problems SOLUTION 2 Begin with (xy) 2 = x y 1 Differentiate both sidesExpand x^3 y^3 z^3 plot x^3 y^3 z^3 factor x^3 y^3 z^3 complex We can write this expression as x3 − (2y)3 The formula for factorizing the Difference of two Cubes is a3 −b3 = (a −b)(a2 ab b2) In x3 −(2y)3, a = x b = 2y x3 −(2y)3 = (x −2y) ⋅ (x2 (x ⋅ 2y) (2y)2)
Solved Factor The Polynomial Completely X 3y 2x 2y 2 Xy 3
