Questions: Factor. [ u^2+12 u+36 ]

Factor. [ u^2+12 u+36 ]
Transcript text: Factor. \[ u^{2}+12 u+36 \]
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Solution

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Solution Steps

Step 1: Identify the quadratic expression

The given expression is a quadratic in the form \( u^{2} + 12u + 36 \).

Step 2: Check if it is a perfect square trinomial

A perfect square trinomial has the form \( (u + a)^{2} = u^{2} + 2au + a^{2} \). Compare this with the given expression:

  • \( 2a = 12 \) → \( a = 6 \).
  • \( a^{2} = 36 \), which matches the constant term.
Step 3: Factor the expression

Since the expression is a perfect square trinomial, it can be factored as: \[ (u + 6)^{2}. \]

Final Answer

\(\boxed{(u + 6)^{2}}\)

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