SOLUTION: 1. Why do you call the product of the sum and the difference of the same two terms the difference between two squares? I need your help on our topic about the Product of the sum

Question 624445: 1. Why do you call the product of the sum and the difference of the same two terms the difference between two squares?
I need your help on our topic about the Product of the sum and the difference of the same two terms. Please answer my question immediately. Thanks in advance!
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Just did that.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula tells you so.
a^2 - b^2 = (a-b) * (a+b)
that's the product of the sum and the difference of the same 2 terms and it is equal to the difference of each term squared.
if you multiply (a-b) * (a+b) you will get:
a^2 + ab - ab - b^2
the 2 middle terms cancel out and you are left with:
a^2 - b^2
it's nothing more than that.
it just puts into words what the formula is showing you.
with multiplication of (a+b) * (a-b) you are using the distributive property of multiplication.
(a-b) * (a+b) is equal to:
a * (a+b) - b * (a+b) which is equal to:
a*a + a*b - b*a - b*b which results in:
a^2 + ab - ab - b^2 which results in:
a^2 - b^2 because ab and -ab cancel out.
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