Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
3.6k views
in Polynomials by (65.2k points)

Evaluate the following using suitable identities :
(i) (99)3
(ii) (102)3
(iii) (998)3

1 Answer

+1 vote
by (65.5k points)
selected by
 
Best answer

(i) (99)3 = (100 – 1)3 

As per Identity, 

(a – b)3 = a3 – b3 – 3ab(a – b) 

(100 – 1)3 = (100)3 – (1)3 – 3(100)(1)(100- 1) 

(99)3 = 1000000 – 1 – 300(100 – 1) 

= 1000000 – 1 – 30000 + 300 = 970299 

∴ (99)3 = 970299 

(ii) (102)3 = (100 + 2)3 

As per Identity,

(a + b)3 = a3 + b3 + 3ab(a + b) 

(100 + 2)3 = (100)3 + (2)3 + 3( 100)(2)( 100 + 2) 

= 1000000 + 8 + 600( 100 + 2) 

= 1000000 + 8 + 60000 + 1200 (100 + 2)3 

= 1061208 

∴ (102)3= 1061208 

(iii) (998)3 = (1000 – 2)3 

As per Identity, 

(a – b)3 = a3 – b3 – 3ab(a – b) 

(1000 – 2)3 = (1000)3 – (2)3 – 3( 1000) (2)(1000 – 2) 

= 1000000000 – 8 – 6000(1000 – 1) 

= 1000000000 – 8 – 6000000 + 6000 

= 994005992 

∴ (998)3 = 994005992

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...