Question

cube of 98 without multiplying​

Answer 1

To Find :- cube of 98 without multiplying ?

Solution :-

98 can be written as (100 - 2) .

So,

→ (98)³

→ (100 - 2)³

comparing (a - b)³ = a³ - b³ - 3ab(a - b) , we get,

• a = 100
• b = 2

Therefore,

→ (100)³ - (2)³ - 3 * 100 * 2 * (100 - 2)

→ 1000000 - 8 - 600 * 98

→ 1000000 - 8 - 58800

→ 1000000 - 58808

→ 941,192 (Ans.)

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow\text{ a digit 98.}$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow\text{ cube of 98 without actual multiplication}$

✯IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\: (a-b)^3= a^3-b^3-3ab(a-b)\:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\sf\therefore\text{ 98 can be written as 100-2}$

$\sf\therefore cubing\: (100-2)$

$\sf\dashrightarrow (100-2)^3$

$\sf\therefore\text{ solving these by using given identity ,}$

$\sf\dashrightarrow (100-)^3= (100)^2-(2)^3-3(100)(2)(100-2)$

$\sf\implies 1000000-8-300(2)(98)$

$\sf\implies 1000000-8-600(98)$

$\sf\implies 999992-58800$

$\sf\implies 941192$

$\large{\boxed{\bf{ \star\:\: (98)^2= 941192\:\: \star}}}$

$\large\underline\bold{THE\:CUBE\:OF\:98\:IS\:\:\: 941192}$

________________