SOLUTION: Discuss whether the statement, (x + y)3 is equivalent to x^3 + y^3, is true or not. Identify a pair of values of x and y for which this statement is true and another pair of

Algebra ->  Systems-of-equations -> SOLUTION: Discuss whether the statement, (x + y)3 is equivalent to x^3 + y^3, is true or not. Identify a pair of values of x and y for which this statement is true and another pair of       Log On


   

Question 359427: Discuss whether the statement, (x + y)3 is equivalent to x^3 + y^3, is true or not.
Identify a pair of values of x and y for which this statement is true and another pair of values for which it is not true.


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2By%29%5E3=x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3
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.
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%28x%2By%29%5E3=x%5E3%2By%5E3 when
3x%5E2y%2B3xy%5E2=0
highlight%28x=-y%29
.
.
.
Example, x=5, y=-5
%28x%2By%29%5E3=0
x%5E3%2By%5E3=125-125=0
%28x%2By%29%5E3=x%5E3%2By%5E3
.
.
.
Counterexample, x=5,y=5
%28x%2By%29%5E3=10%5E3=1000
x%5E3%2By%5E3=125%2B125=250
%28x%2By%29%5E3%3C%3Ex%5E3%2By%5E3