Answer
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Step 1:I'll solve this step-by-step using the guidelines you specified:
Step 2:: Recognize the form of the quadratic expression
• The expression is $$x^{2} - 8x + 16
• This looks like a perfect square trinomial
Step 3:: Check if it can be factored by grouping
• We'll look for two numbers that multiply to $$16$$ and add to $$-8
Step 4:: Rewrite the middle term
• $$x^{2} - 8x + 16 = x^{2} - 2(4)x + (4)^{2}
• This matches the pattern a^{2} - 2ab + b^{2}
Step 5:: Apply the perfect square trinomial formula
• $$x^{2} - 8x + 16 = (x - 4)^{2}
Step 6:: Verify the factorization
• Expand $$(x - 4)^{2}
• = x^{2} - 8x + 16 • This matches our original expression
Final Answer
x^{2} - 8x + 16 = (x - 4)^{2}
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