If a + b = 1, find the value of a^{3}+b^{3}-a b- (a^{2}-b^{2} )^{2}

SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 68 of 100

Marks: +1, -0

a + b = 1

, find the value of

a^{3}+b^{3}-a b- (a^{2}-b^{2} )^{2}

Solution:

(3)

a + b = 1

(Given)
Expression

=a^{3}+b^{3}-a b- (a^{2}-b^{2} )^{2}

=(a+b)\ (a^{2}-a b+b^{2} )-a b- (a^{2}-b^{2} )^{2}

= (a^{2}-a b+b^{2} )-a b-(a+b)^{2}(a-b)^{2}

=a^{2}-a b+b^{2}-a b- (a^{2}-2 a b+b^{2} )

=a^{2}-2 a b+b^{2}-a^{2}+2 a b-b^{2}=0

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