x^2 – 8x + 16
(x – 4)^2
The expression x^2 – 8x + 16 is a quadratic trinomial. Here’s how to factor it:
1. First, determine what two numbers when multiplied together give you 16, and when added together give you -8. These numbers are -4 and -4, since (-4) * (-4) = 16, and (-4) + (-4) = -8.
2. Replace the middle term, -8x, with the two values from step 1:
x^2 – 4x – 4x + 16
3. Group the first two terms and the last two terms:
(x^2 – 4x) + (-4x + 16)
4. Factor out the GCF (greatest common factor) from each group:
x(x – 4) – 4(x – 4)
5. Notice that both groups have the same factor, so you can combine them into one expression:
(x – 4)(x – 4)
6. Simplify to get the final answer:
(x – 4)^2
Therefore, x^2 – 8x + 16 can be factored as (x – 4)^2.
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