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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)

Top Answer

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dylee | High School Teacher | (Level 1) eNoter

Posted on

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____________________  (Sorry for the poor drawing....)

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

Posted on

Nice!! I atleast understood it.

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