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Without actually calculating the cubes, find the value of each of the following: (i) (−12)^3 + (7)^3 + (5)^3 (ii) (28)^3 + (−15)^3 + (−13)^3
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07/07/2021 11:07 am
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Without actually calculating the cubes, find the value of each of the following:
(i) (−12)^{3 }+ (7)^{3 }+ (5)^{3}
(ii) (28)^{3 }+ (−15)^{3 }+ (−13)^{3}
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07/07/2021 11:09 am
(i) (−12)^{3}+(7)^{3}+(5)^{3}
Let a = 12
b = 7
c = 5
We know that if x + y + z = 0, then x^{3}+y^{3}+z^{3}=3xyz.
Here, −12 + 7 + 5 = 0
(−12)^{3}+(7)^{3}+(5)^{3 }= 3xyz
= 3 × 12 × 7 × 5
= 1260
(ii) (28)^{3}+(−15)^{3}+(−13)^{3}
(28)^{3}+(−15)^{3}+(−13)^{3}
Let a = 28
b = −15
c = −13
We know that if x + y + z = 0, then x^{3}+y^{3}+z^{3 }= 3xyz.
Here, x + y + z = 28 – 15 – 13 = 0
(28)^{3}+(−15)^{3}+(−13)^{3 }= 3xyz
= 0 + 3(28)(−15)(−13)
= 16380
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