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(A) We know the algebraic identity: If $x + y + z = 0$,then $x^{3} + y^{3} + z^{3} = 3xyz$.Given expression: $(14)^{3} + (27)^{3} - (41)^{3}$.This can

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$-46494$

Vedclass · Answer

(A) We know the algebraic identity: If $x + y + z = 0$,then $x^{3} + y^{3} + z^{3} = 3xyz$.Given expression: $(14)^{3} + (27)^{3} - (41)^{3}$.This can be rewritten as: $(14)^{3} + (27)^{3} + (-41)^{3}$.Let $x = 14$,$y = 27$,and $z = -41$.Check the sum: $x + y + z = 14 + 27 + (-41) = 41 - 41 = 0$.Since the sum is $0$,the expression equals $3xyz$.Value $= 3 	imes (14) 	imes (27) 	imes (-41)$.Value $= 3 	imes 378 	imes (-41) = 1134 	imes (-41) = -46494$.

Without actually calculating the cubes,find the value of each of the following:
$(14)^{3} + (27)^{3} - (41)^{3}$

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Without actually calculating the cubes,find the value of each of the following:$(14)^{3} + (27)^{3} - (41)^{3}$