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Brady incorrectly factored x^2 - 10x + 25 by trying to factor it as a difference of squares. However, x^2 - 10x + 25 is not a perfect square trinomial. The correct way to factor it is to recognize that it can be written as (x - 5)^2, not (x + 5)(x - 5).
For 16c^2 - 9, Brady tried to factor it as a difference of squares which is correct, but made a mistake in the final step. The correct factorization should be (4c)^2 - 3^2 = (4c + 3)(4c - 3), not (4c - 3)^2.
Therefore, the correct factorizations are:
x^2 - 10x + 25 = (x - 5)^2
16c^2 - 9 = (4c + 3)(4c - 3)