Which shows 422 - 382 being evaluated using the difference of perfect squares method?

422 - 382 = (1,764 - 1,444) (1,764 + 1,444) = 1,026,560

422 - 382 = 84 - 76 = 8

422 - 382 = (42 - 38) 2 = (4) 2 = 16

422 - 382 = (42 + 38) (42 - 38) = (80) (4) = 320

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