Question

Evaluate each of the following using suitable identity: (i)(97)³ (ii)(1002)³

Answer 1

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Answer 2

Answer:

(97)

3

=912673

Step-by-step explanation:

Given : Expression (97)^3(97)

3

To find : Evaluate the expression ?

Solution :

Write the expression as,

(97)^3=(100-3)^3(97)

3

=(100−3)

3

Applying identity, (a-b)^3= a^3-b^3-3a^2b+3ab^2(a−b)

3

=a

3

−b

3

−3a

2

b+3ab

2

Here, a=100 and b=3

Substitute the values,

(100-3)^3=(100)^3-(3)^3-3(100)^2(3)+3(100)(3)^2(100−3)

3

=(100)

3

−(3)

3

−3(100)

2

(3)+3(100)(3)

2

(97)^3=1000000-27-90000+2700(97)

3

=1000000−27−90000+2700

(97)^3=912673(97)

3

=912673

Therefore, (97)^3=912673(97)

3

=912673