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x2 + 16 - 8x is a perfect square. First, let's correctly arrange the terms:
= x2 - 8x + 16
We can see that the last term is equal to the square of half the coefficient of the second term. This tells us that it's a perfect square, and we can simply say:
= (x - 4)2
We can also work this out using the usual technique for finding factors of quadratic expressions. We need two numbers that add to make -8 and multiply to make 16. That would be two of the same number, -4.:
= x2 - 4x - 4x + 16
= x(x - 4) - 4(x - 4)
= (x - 4)(x - 4)
= (x - 4)2
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