Question

(ii) (999)3 polynomial for this sum​

Answer 1

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