Find the value of x^{3}+y^{3}-12xy+64,when x+ | vedclass

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(B) Given expression: $x^{3}+y^{3}-12xy+64$.We know the algebraic identity: $a^{3}+b^{3}+c^{3}-3abc = (a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)$.Here,let $a

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(B) Given expression: $x^{3}+y^{3}-12xy+64$.We know the algebraic identity: $a^{3}+b^{3}+c^{3}-3abc = (a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)$.Here,let $a=x$,$b=y$,and $c=4$.Then the expression becomes $x^{3}+y^{3}+4^{3}-3(x)(y)(4) = x^{3}+y^{3}+64-12xy$.Substituting $a+b+c = x+y+4$ into the identity:Since $x+y = -4$,we have $x+y+4 = -4+4 = 0$.Therefore,$x^{3}+y^{3}-12xy+64 = (0)(x^{2}+y^{2}+16-xy-4y-4x) = 0$.

Find the value of $x^{3}+y^{3}-12xy+64$,when $x+y=-4$.

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