Question

Find the value of $<var>x^{3} - y^{3} </var>$ if x-y= -7 and xy = -10..

Answer 1

x - y = -7  & xy = -10
(x - y)³ = x³ - y³ - 3xy(x - y)
(-7)³ = x³ - y³ - 3(-10)(-7)
-343 = x³ - y³ -210
x³ - y³ = -133

Answer 2

x³-y³ = (x-y)(x²+xy+y²)   this is the formula 
       given x-y = -7 and xy = -10 
but we know that 
x²+y²=(x-y)² +2xy
        = (-7)² +2(-10)
        = 49-20
        =29
   substitute these in the above x³-y³ formula then we get 
 x³-y³ = (-7)(29-10)
        = (-7)(19)
         = -133 
This is answer