Question

please explain this and answer ​

Answer 1

Step-by-step explanation:

a) (998)^3

=(1000 - 2)^3

=(1000)^3 - (2)^3 - { 3 × 1000 × 2 (1000 - 2)}

◆ On the formula, (a - b )^3 = a^3 -b^3 - 3ab(a - b)

=1000000000 - 8 - { 6000 (1000 - 2)}

=1000000000 - 8 - (6000000 - 12000)

=1000000000 - 8 -6000000 + 12000

=1000000000 + 12000 - 8 - 6000000

=1000012000 - 6000008

=994011992.

b) (10.2)^3

=(10 + 0.2)^3

=(10)^3 + (0.2)^3 + { 3 × 10 ×0.2 (10 + 0.2)}

=1000 + 0.008 + { 6 (10 + 0.2)}

=1000 + 0.008 + 60 +1.2

=1061.208

c) (998)^2 - 4

=(998)^2 - (2)^2

=(998 + 2)(998 - 2)

=1000 × 996

=996000

d) (999)^2 - 1

=(999)^2 - (1)^2

=(999 + 1) (999 - 1)

=1000 × 998

=998000

e) (-25)^3 + (10)^3 + (15)^3

Here a = -25 , b = 10 , c = 15

= 3 × a × b × c

= 3 × (-25) × 10 × 15

= (-75) × 150

= -11250

f) 10.2 × 9.8

= (10 + 0.2) × (10 - 0.2 )

=(10)^2 - (0.2)^2

◆ On the formula , (a^2 - b^2 ) = (a + b)(a - b)

=100 - 0.04

=99.96