Question

3. Evaluate using suitable identity :
a) 〖(102)〗^3 b) 〖(998)〗^3

Answer 1

$\mathfrak{\huge{\pink{\underline{\underline{AnswEr:-}}}}}$

It is known that,

(a+b)3=a3+b3+3ab(a+b)and(a−b)3=a3−b3−3ab(a−b)

(i) (102)3 = (100 + 2)3

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

= 1000000 + 8 + 600 (102)

= 1000000 + 8 + 61200

= 1061208

(ii) (998)3= (1000 − 2)3

= (1000)3 − (2)3 − 3(1000) (2) (1000 − 2)

= 1000000000 − 8 − 6000(998)

= 1000000000 − 8 − 5988000

= 1000000000 − 5988008

= 994011992

Answer 2

Answer:

$\huge{\mathbb{Answer : -}}$

$\huge{\mathbb{ANSWER1 : -}}$ (102)3 = (100 + 2)3

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

= 1000000 + 8 + 600 (102)

= 1000000 + 8 + 61200

= 1061208

$\huge{\mathbb{ANSWER 2: -}}$(998)3= (1000 − 2)3

= (1000)3 − (2)3 − 3(1000) (2) (1000 − 2)

= 1000000000 − 8 − 6000(998)

= 1000000000 − 8 − 5988000

= 1000000000 − 5988008

= 994011992