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AP TET Paper 1 Model Test 3

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Question : 98 of 150

Marks: +1, -0

Evaluate 999^{3}.

997005999
997002999
997003999
997004999

Solution:

Concept:

Use the identity

(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3

with

a = 1000

and

b = 1

.

Explanation:

Write

999 = 1000 - 1

.

Cube both sides:

999^3 = (1000 - 1)^3

.

Apply the identity:

(1000)^3 - 3(1000)^2(1) + 3(1000)(1)^2 - (1)^3

.

Compute:

1\,000\,000\,000 - 3\,000\,000 + 3\,000 - 1 = 997\,002\,999

.

Answer:

Option B: 997002999

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