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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____________________ (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)