Evaluate (999) cube.
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Answer:
999)
3
=997002999
Step-by-step explanation:
Given : Expression (999)^3(999)
3
To find : Evaluate expression using suitable identities?
Solution :
We can write the expression as
(999)^3=(1000-1)^3(999)
3
=(1000−1)
3
Now, Expand using identity,
(a-b)^3=a^3-b^3-3ab(a-b)(a−b)
3
=a
3
−b
3
−3ab(a−b)
Substitute, a=1000 and b=1
(1000-1)^3=(1000)^3-1^3-3(1)(1000)(1000-1)(1000−1)
3
=(1000)
3
−1
3
−3(1)(1000)(1000−1)
(1000-1)^3=1000000000-1-(3000)(999)(1000−1)
3
=1000000000−1−(3000)(999)
(1000-1)^3=1000000000-1-2997000(1000−1)
3
=1000000000−1−2997000
(1000-1)^3=997002999(1000−1)
3
=997002999
Therefore, (999)^3=997002999(999)
3
=997002999
Answer:
Thanks for your answer
Step-by-step explanation:
Cutie