Proving a^2 - b^2 = (a+b)(a-b) with Factorization

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To prove that a^2 - b^2 = (a+b)(a-b) using factorization, start with the expression a^2 - b^2. It can be rewritten by adding and subtracting ab, resulting in a^2 - b^2 + ab - ab. This manipulation allows for regrouping into a(a+b) - b(a+b), which simplifies to (a+b)(a-b). The key concept is recognizing that adding zero in the form of ab - ab does not change the expression, facilitating the factorization process.
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Hello, how can I prove using factorization that a^2 - b^2 = (a+b)(a-b) ?

a*a - b*b I should get something like a(a-b)+b(a-b) but how ?

thanks
 
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a2 - b2 == a2 - b2 + ab - ab == a2 + ab - b2 - ab == a(a+b) - b(a+b) == ?
 
Ok but how do I get a^2 - b^2 + ab - ab from a^2 - b^2 ?
 
Add ab and subtract ab.
 
scientifico said:
Ok but how do I get a^2 - b^2 + ab - ab from a^2 - b^2 ?

HallsofIvy said:
Add ab and subtract ab.

You can always add zero to any expression (here in the form of ab + (-ab), and you can always multiply an expression by 1.
 
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