# 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?

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 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.