Why doesn't the cal work with factoring? EX: factor a^2 - 64. The calc comes back with a^2-64 and that is not correct. Also the calc does not reduce to lowest terms - why not?

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This is a difference of two perfect squares problem.  The answer is  the sum and difference of the squares: (a+8)(a-8) = a^2-64) because when tyou carry out the FOIL multiplication of the left side the inside and outside products cancel each other.