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# a^2 -b^2 = (a+b)(a-b)

## Question

All of you know that a2 - b2 = (a+b)(a-b)

I know only two method to prove it.

a2 - b2 a2 - b2

a2 - b2 + ab - ab a2 - b2 + 2ab -2ab -2b2

a2 + ab - ab - b2 (a+b)2 - 2b(a+b)

a(a+b) - b(a+b) (a+b)(a+b) - 2b(a+b)

(a-b)(a+b) (a+b)(a+b-2b)

(a+b)(a-b)

Apart form these two method are there any other method to prove it.

Edited by Utkrisht123

## Recommended Posts

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Can't you prove it just by expanding the product?

All the steps are reversible, so going either direction accomplishes the same thing.

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(a+b)(a-b)=a(a-b)+b(a-b)=a^2-ab+ba-b^2=a^2-b^2

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Perhaps, OP is looking for this:

Suppose, a = b + k, then k = a - b.

a2 - b2 = (b+k)2 - b2 = b2 + 2bk + k2 - b2= k(2b+k) = k(b+k+b)=(a-b)(a+b)

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a2 - b2

(a + b - b)2 - b2

(a + b)2 + b2 - 2b(a + b) - b2

(a + b)2 - 2b(a + b)

(a + b)(a + b -2b)

(a + b)(a - b)

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In post # 1 in the right-hand column under

"a^2 - b^2,"

the next line should be

"a^2 + b^2 + 2ab - 2ab - 2b^2."

Edited by Perhaps check it again

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