Evaluate the following using suitable identities:
(i) (99)3 (ii) (102)3 (iii) (998)3
Solution:
We will use the following algebraic Identities to evaluate the given expressions.
(x + y)3 = x3 + y3 + 3xy(x + y)
(x - y)3 = x3 - y3 - 3xy(x - y)
(i) (99)3 = (100 - 1)3
Identity: Here we can use (x - y)3 = x3 - y3 - 3xy(x - y)
Let us substitute x = 100, y = 1
(99)3 = (100)3 - (1)3 - 3(100)(1)(100 - 1)
= 1000000 - 1 - 300 × 99
= 999999 - 29700
= 970299
(ii) (102)3 = (100 + 2)3
Identity: (x + y)3 = x3 + y3 + 3xy(x + y)
Let us substitute x = 100, y = 2
(102)3 = (100)3 + (2)3 + 3(100)(2)(100 + 2)
= 1000000 + 8 + 600 × 102
= 1000008 + 61200
= 1061208
(iii) (998)3 = (1000 - 2)3
Identity: (x - y)3 = x3 - y3 - 3xy(x - y)
Let us substitute x = 1000, y = 2
(998)3 = (1000)3 - (2)3 - 3(1000) (2) (1000 - 2)
= 1000000000 - 8 - 6000 × 998
= 999999992 - 5988000
= 994011992
☛ Check: NCERT Solutions for Class 9 Maths Chapter 2
Video Solution:
Evaluate the following using suitable identities: (i) (99)³ (ii) (102)³ (iii) (998)³
NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.5 Question 7:
Summary:
The evaluated values of the following (99)3, (102)3, and (998)3 using suitable identities are 970299, 1061208, and 994011992 respectively.
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