Question
\( 1 \leftarrow \left\lvert\, \begin{array}{l}\text { Determine whether the expression is a trinomial square. } \\ a^{2}-10 a+25 \\ \text { Is the expression a trinomial square? } \\ \text { Yes } \\ \text { No }\end{array}\right. \)
Ask by Beck Thornton. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression \( a^{2} - 10a + 25 \) is a trinomial square because it can be written as \( (a - 5)^2 \).
Solution
The given expression is a² - 10a + 25.
Recall that a perfect square trinomial takes the form (a - b)² = a² - 2ab + b².
Comparing, we see:
• The coefficient of a is -10, which suggests 2b = 10, so b = 5.
• Checking the constant term, b² = 25, which matches.
Therefore, a² - 10a + 25 = (a - 5)².
Yes, the expression is a trinomial square.
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Simplify this solution Beyond the Answer
Absolutely, let’s dive into it! The expression \( a^{2} - 10a + 25 \) is indeed a trinomial square. To confirm this, you can check if it can be factored into the form \( (a - b)^{2} \). In this case, \( b \) would be \( 5 \) because \( (a - 5)^{2} = a^{2} - 10a + 25 \). So yes, the expression is a perfect square trinomial! Now, wasn’t that a neat little discovery? When dealing with trinomials, remember to look out for perfect squares in the form of \( a^{2} - 2ab + b^{2} \), where \( b \) is the square root of the last term. Identifying these can save you time and effort in algebra! Now you can have fun factoring and solving other expressions like a pro!
