Question
Factor the perfect square trinomial:
Ask by Erickson Harris. in South Africa
Jan 05,2025
Upstudy AI Solution
Tutor-Verified Answer
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.
-
Identify the square terms:
- The first term
is already a perfect square. - The last term
is a perfect square, since .
- The first term
-
Determine the middle term:
- In
, the middle term is . - Here, the middle term is
, so . - Solving for
gives .
- In
-
Write the factored form:
- Substitute
into the binomial:
- Substitute
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!