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Byju's Answer
Standard VIII
Mathematics
Polynomials
Without actua...
Question
Without actually calculating the cubes,find the value of
(-1)
3
+ (-2)
3
+(-3)
3
+(-4)
3
+2(5)
3.
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Solution
1^3 + 2^3 + ....... + n^3 = [n (n+1) / 2]^2
So, (-1)^3 + (-2)^3 + (-3)^3 + (-4)^3 + 2(5)^3
= - [ 4 (4+1) / 2]^2 + 2(5)^3
= - 4(5)^2 + 2(5)(5)^2
= - 4 (5)^2 + 10 (5)^2
= 6 (5)^2
= 6(25)
= 150
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