Answer:
Option D
422 − 382 = (42 + 38)(42 − 38) = (80)(4) = 320
Step-by-step explanation:
Let us consider the following:-
(a + b)(a - b)
a^2 - ab + ab - b^2
Since -ab+ab = 0
Then what will be left is:
a^2 - b^2
This is a proof that:
(a + b)(a - b) is the same as a^2 - b^2
Let's use actual figures to show this:-
(5 + 3)(5 - 3)
25 - 15 + 15 - 9
- 15+15 is the same as + 15 - 15 = 0
We will then be left with:
25 - 9 = 16
The fact is that we can achieve this same result from the product of their sum and difference.
Since 5 + 3 = 8 and 5 - 3 = 2
Then: (8)(2) = 16
Now, back to the question:
42^2 - 38^2 can be evaluated using the difference of perfect square method which is simply finding their sum and their difference and then multiplying the two results:
422 − 382 = (42 + 38)(42 − 38)
42 + 38 = 80
42 - 38 = 4
(80)(4) = 320
