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How to prove a^2-b^2=(a-b)(a+b)

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rahulsk | Student, Grade 10 | (Level 1) Honors

Posted June 3, 2012 at 1:12 PM via web

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How to prove a^2-b^2=(a-b)(a+b)

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dylee | High School Teacher | (Level 1) eNoter

Posted June 4, 2012 at 11:40 AM (Answer #1)

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Imagine that there are two squares overlapped like that
Let the one side of big square be a, and the side of small square be b.

If we subtract 'b^2 from 'a^2, this would mean subtracting the area of small square from the big square.

Therefore, the result of 'a^2 - 'b^2 would be equal to he remaining area. The remaining area is 'a*(a-b) + 'b*(a-b) = (a+b)*(a-b)

 

'a^2-'b^2 = '(a+b)*(a-b)

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 3, 2012 at 1:30 PM (Answer #2)

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It can be proved that a^2 - b^2 = (a - b)(a + b) by multiplying the terms on the right.

Multiply (a - b)(a + b) by opening the brackets

=> a*a + a*b - b*a - b^2

=> a^2 + ab - ab - b^2

=> a^2 - b^2

This proves that a^2 - b^2 = (a - b)(a + b)

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rahulsk | Student, Grade 10 | (Level 1) Honors

Posted October 17, 2012 at 2:48 PM (Answer #6)

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Nice!! I atleast understood it.

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