Question

50³ + 3 x 50² x 2 + 3 x 50 x 2² + 2³ =_____________. {choose correct answer}
(A) (48)³ (B) (53)³ (50)³ (D) (52)³​

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

Here,

We need to find the value of the above sum but in some other way using identities (For easier calculation).

GiveN:

50³ + 3 x 50² x 2 + 3 x 50 x 2² + 2³

How to do?

Considering that 50 and 2 has some relation between them, Let 50 = x and 2 = y. Then,

= 50³ + 3 x 50² x 2 + 3 x 50 x 2² + 2³

= x³ + 3x²y + 3xy² + y³

This is the formula for the Identity:

• (x + y)³ = x³ + 3x²y + 3xy² + y³

Then,

= x³ + 3x²y + 3xy² + y³

= (x + y)³

Now putting the value of x and y:

= (50 + 2)³

= (52)³

Thus,

The correct answer of the sum is: Option D

$\huge{ \boxed{ \sf{ \purple{ {(52)}^{3} }}}}$

Answer 2

Question

50³ + 3 x 50² x 2 + 3 x 50 x 2² + 2³ =_____________. {choose correct answer}

(A) (48)³ (B) (53)³ (50)³ (D) (52)³

Solution

50³ + 3×50²×2 + 3×50×2² + 2³

= 125000+15000+600+8

= 140608

= 3√140608

= 52

Ans:- So the correct answer is (52)³.