Without actually calculating the cubes,find t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$-46494$

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:
$(14)^{3} + (27)^{3} - (41)^{3}$

Similar Questions

Expand $(11 x+18)(11 x-18)$.

Expand each of the following,using suitable identities: $\left[\frac{1}{4} a-\frac{1}{2} b+1\right]^{2}$

Evaluate the following using suitable identities: $(995)^{3}$

Give a possible expression for the length of a side of a square whose area is $(9x^2 + 30x + 25)$ square units, where $(x > 0)$.

Evaluate the following using suitable identities: $(102)^{3}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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