If x-y = 4 and xy = 21 then find the value of x 3 - y 3
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x - y = 4
xy = 21
x^3 - y^3 = ( x - y ) ( x^2 + xy + y^2 )
( x - y )^2 = 4^2
x^2 + y^2 - 2xy = 16
x^2 + y^2 = 16 + 2xy
x^2 + y^2 = 16 + 2*21
x^2 + y^2 = 58
Now substituting all the values
x^3 - y^3 = ( x - y ) ( x^2 + y^2 + xy )
= 4 * ( 58 + 21 )
= 4 * 79
= 316.
xy = 21
x^3 - y^3 = ( x - y ) ( x^2 + xy + y^2 )
( x - y )^2 = 4^2
x^2 + y^2 - 2xy = 16
x^2 + y^2 = 16 + 2xy
x^2 + y^2 = 16 + 2*21
x^2 + y^2 = 58
Now substituting all the values
x^3 - y^3 = ( x - y ) ( x^2 + y^2 + xy )
= 4 * ( 58 + 21 )
= 4 * 79
= 316.
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