SOLUTION: A student says he noticed that 39 * 41 = 40 * 40 � 1, and 59 * 61 = 60 * 60 � 1. He wants to know if this pattern continues. How do you respond?

Question 174067: A student says he noticed that 39 * 41 = 40 * 40 � 1, and 59 * 61 = 60 * 60 � 1. He wants to know if this pattern continues. How do you respond?
Answer by loni(3) (Show Source): You can put this solution on YOUR website!
OK, that is so:
(a-b)*(a+b)=a^2+ab-ab-b^2 ; ab-ab=0 , so (a-b)*(a+b)=a^2-b^2.
In this case b is always b=1 so:
(a-1)*(a+1)=a^2-1^2; 1^2=1, (a-1)*(a+b)=a^2-1.
Now when a=40, b=1,
(40-1)*(40+1)=40^2-1^2;
(60-1)*(60+1)=60^2-1^2 etc.....
I hope you like the answer and I am sorry for my bad English.
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