Question

Factor the perfect square trinomial:

Ask by Erickson Harris. in South Africa
Jan 05,2025

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Answer

Solution

The given trinomial is:
To factor this as a perfect square trinomial, we look for a binomial of the form that expands to the given trinomial.
  1. Identify the square terms:
    • The first term is already a perfect square.
    • The last term is a perfect square, since .
  2. Determine the middle term:
    • In , the middle term is .
    • Here, the middle term is , so .
    • Solving for gives .
  3. Write the factored form:
    • Substitute into the binomial:
Final Answer:

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Extra Insights

The expression can be factored as . This is because the trinomial is a perfect square; the middle term (12x) is twice the product of the square root of the first term (x) and the square root of the last term (6), confirming that it can indeed be factored into the square of a binomial.
Another engaging approach to understand factoring perfect square trinomials is to visualize them as geometric squares! If you think of constructing a square with side lengths that increase with each term in the trinomial, you’ll see that corresponds to a square with sides of length —making it easy to see that the area can be represented as . Plus, it’s a great way to appreciate the beauty of algebraic expressions!

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