(3508)^2 - (3510*3508) =

This calls for some factoring

(3508)² - (3510*3508) = (3508)(3508) - (3510)(3508)
= 3508(3508 - 3510)
= 3508(-2)
= -7016

Answer: E

Another approach is to keep track of the units digits only

(3508)² - (3510*3508) = (---6) - (---0)
= -(----4)

Since answer choice E is the only answer with units digit 4, E must be correct.

Cheers,
Brent

(3508)^2 - (3510*3508) = ?

3508 * (3508 - 3510)

3508 * (-2)

-7016

(E)

Let a = 3508 & b = 3510 Or, (a + 2)

So, (3508)^2 - (3510*3508) = a^2 - ab

Or, a^2 - ab = a ( a - b)

Or, a ( a - b) = a (a - a - 2)

Or, a ( a - b) = -2a

THus, Answer must be -2*3508 = -7016 , Answer must be (E)

Factor 3508 from both terms, obtaining:

3508(3508 - 3510)

3508(-2) = -7016

Answer: E

Please could you help me understand how to calculate units place here? I tried solving through this method I am getting units place as 4

Oops, I made a mistake earlier (which I've corrected in the highlighted area above )

When multiplying two integers, the units digit of the entire product will be the same as the units digit of the product of the two units digits.
For example, we know that (7)(2) = 14
This means the product of something like (327)(122) will be -------4

Likewise, the units digit of 3508*3508 will be the unit's digit of (8)(8), which is 4
And the units digit of 3510*3508 will be the unit's digit of (0)(8), which is 0

So, we have (3508)² - (3510*3508) = (---4) - (---0)

Finally we need to recognize that (3508)² < (3510*3508)
So, when we subtract (3510*3508) from (3508)², we will get a NEGATIVE result.
To determine the units digit of this negative result, you can test two values, such that the first number has units digit 4, and the second number has units digit 0 (where the second number is bigger)

For example you could try 4 - 10 = -6 (units digit 6)
Or 4 - 30 = -26 (units digit 6)
Or 24 - 100 = -76 (units digit 6)
Etc

Thank you so much. Now I am understanding better

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