Question

Evaluate the following by using identities (i) (204)^2 (ii) (992)^2


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Answer 1

Answer:

(i) (204)^2=41616

(ii) (992)^2 =984064

Step-by-step explanation:

i) (204)^2 = (200 + 4 )^2    [splitting (204)^2 as (200+4)^2 in the form of the identity (a+b)^2]

               = (200)^2+2*200*4+4^2

               =40000+1600++16

                =41616  

ii) (992)^2= (990+2)^2     [splitting (992)^2 as (990+2)^2 in the form of the                   identity (a+b)^2]

                =(990)^2+2*990*2+2^2

                 =980100+3960+4

                  =984064

Answer 2

☯ SolutioN :

We can write (204)² as (200 + 4)²

Here, we can use a identity :

$\Large{\implies{\boxed{\boxed{\sf{(a + b)^2 = a^2 + b^2 + 2ab}}}}}$

★ Putting Values ★

$\sf{\dashrightarrow (204)^2 = 200^2 + 4^2 + 2(200)(4)} \\ \\ \sf{\dashrightarrow (204)^2 = 40000 + 16 + 1600} \\ \\ \sf{\dashrightarrow (204)^2 = 40000 + 1616} \\ \\ \sf{\dashrightarrow (204)^2 = 41616} \\ \\ \Large{\implies{\boxed{\boxed{\sf{41616}}}}}$

↪ For verification put value of 204².

$\sf{\dashrightarrow 41616 = 41616} \\ \\ \bf{Hence \: Verified}$

$\rule{200}{2}$

We can write (992)² as (1000 - 8)²

Here, we can use a identity :

$\Large{\implies{\boxed{\boxed{\sf{(a - b)^2 = a^2 + b^2 - 2ab}}}}}$

★ Putting Values ★

$\sf{\dashrightarrow (992)^2 = 1000^2 + 8^2 - 2(1000)(8)} \\ \\ \sf{\dashrightarrow (992)^2 = 1000000 + 64 - 16000} \\ \\ \sf{\dashrightarrow (992)^2 = 1000064 - 16000} \\ \\ \sf{\dashrightarrow (992)^2 = 998464} \\ \\ \Large{\implies{\boxed{\boxed{\sf{984064}}}}}$

↪ For verification put value of 992².

$\sf{\dashrightarrow 984064 = 984064} \\ \\ \bf{Hence \: Verified}$