Question

23: Evaluate each of the following using suitable identities:
(i) (104)
(i) (999)3​

Answer 1

Step-by-step explanation:

(i) (104)^3

We write it as 100 + 4

Using (a+b)^3 = a^3 + b^3 + 3ab(a+b)

Let a be 100 and b be 4

= (100)^3 + (4)^3 + 3×100×4(100+4)

= 1000000 +64 + 1200(104)

= 1000000 + 64 + 124800

= 1124864

(ii) We can write (999)^3 as (1000 - 1)^3

Now applying the same method used above

a = 1000 and b = 1

= (1000)^3 - (1)^3 - 3 × 1000 × 1(1000-1)

= 1000000000 - 1 - 2997000

=997002999

Answer 2

Answer:

(i) (104) = (100+4)

Using Identity (a+b)² = a² + b² + 2ab

Where, a= 100

b=4

(a+b)²= (100)² + (4)² + 2 (100) (4)

(a+b)²= 10,000 + 16 + 200 + 8

= 10,224. Is your Answer!!

(ii) (999)³ = (1000-1)³

Using Identity a-b³ = (a-b) (a²+b²+ab)

Where a=1000

b=1

a-b³= (1000-1) (1000²+1²)+( 1000×1)

= 999 (1000000+1+100)

= 999×1000101

= 999,100,899 Is your Answer!!