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

[scientifico]

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

 

[sjb-2812]

a² - b² == a² - b² + ab - ab == a² + ab - b² - ab == a(a+b) - b(a+b) == ?

 

[scientifico]

Ok but how do I get a^2 - b^2 + ab - ab from a^2 - b^2 ?

 

[HallsofIvy]

Add ab and subtract ab.

 

[Mark44]

Ok but how do I get a^2 - b^2 + ab - ab from a^2 - b^2 ?

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.