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This step is not the source of the fallacy.

This follows from the previous step (2 a^2 - 2 ab = a^2 - ab) by factoring out the 2 from the left-hand side and factoring out a 1 from the right-hand side.

The distributive law says that x(y+z) = xy + xz for all numbers x, y, and z, and the factorization 2 a^2 - 2 ab = 2 (a^2 - ab) is simply an application of this to the particular case x=2, y=a^2, and z = -ab.

Writing a^2 - ab = 1(a^2 - ab) is legitimate since multiplying any number by 1 leaves the number unchanged.

Why don't you go back to the list of steps in the proof and see if you can identify which one is wrong, now that you know it isn't this one?
This page last updated: May 26, 1998
Original Web Site Creator / Mathematical Content Developer: Philip Spencer
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