An algebra problem by Wahyu August
Algebra
Level
2
If ab < 0, then the relation in sizes of (a – b)^2 and (a + b)^2 is
(a – b)^2 = (a + b)^2
(a – b)^2 < (a + b)^2
Not determined
(a – b)^2 > (a + b)^2
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1 solution
If a b < 0 , that implies that a b is negative.
Expanding ( a − b ) 2 we get a 2 − 2 a b + b 2 , where as for ( a + b ) 2 we have a 2 + 2 a b + b 2 .
a 2 and b 2 are positive (assuming that they're real).
Therefore ( a − b ) 2 > ( a + b ) 2 .