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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

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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

   

 

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Answer:

Option D

Step-by-step explanation:

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