Question

using identities evaluate (501×502)

Answer 1

501×502
= (500+1)(500+2)
= 250000+1000+500+2
=251502

Answer 2

Given:

501×502

To find:

The 501×502 using identities.

Solution:

Using identities, 501×502 is equal to 251,502.

As given, we have,

$501 \times 502$

This can be written as

$(500 + 1) \times (500 + 2) \: \: \: (i)$

Now,

As we know that

$(x + a)(x + b) = {x}^{2} + \: (a + b)x \: + ab$

On comparing (i) with the above identity, we have,

x = 500, a = 1 and b = 2

So,

We can write (i) as

$({500)}^{2} + (1 + 2)500 + (1 \times 2)$

On solving the above, we get

$= 250000 + 1500 + 2$

$= 251502$

Hence, 501×502 is equal to 251502.