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QuestionMathematics

Factor completely: x^2 −8x+ 16
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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}