Correct Answer:
B. (x+9)²
This question asks to express the given quadratic trinomial as a perfect square.
- Foundational Concept: A perfect square trinomial follows the algebraic identity (a+b)² = a² + 2ab + b² or (a-b)² = a² - 2ab + b².
- Correct Answer ((x+9)²): In the expression x² + 18x + 81, we identify a² as x², so a=x. The constant term 81 is 9², so b=9. We then check the middle term: 2ab = 2 * x * 9 = 18x, which perfectly matches the given expression. Therefore, x² + 18x + 81 is the expansion of (x+9)².
- Why other options are false:
- (x+8)² expands to x² + 16x + 64.
- (x−8)² expands to x² − 16x + 64.
- (x−9)² expands to x² − 18x + 81.
None of these options correctly match both the middle term and the constant term of the original expression.