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

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justaguide eNotes educator| Certified Educator

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)

dylee | Student

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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)

 

rahulsk | Student

Nice!! I atleast understood it.

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