Question
36, Consider the expression. \( x^{2}+3 x y+y^{2} \) If \( x=9 \), and \( y=4 \), what is the value of the expression? A 53 B 121 C 134 D 205
Ask by Matthews Schwartz. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The value of the expression is 205.
**Answer:** D) 205
Solution
To evaluate the expression \( x^{2} + 3xy + y^{2} \) with \( x = 9 \) and \( y = 4 \), follow these steps:
1. **Substitute the given values into the expression:**
\[
(9)^{2} + 3 \times 9 \times 4 + (4)^{2}
\]
2. **Calculate each term:**
\[
9^{2} = 81
\]
\[
3 \times 9 \times 4 = 108
\]
\[
4^{2} = 16
\]
3. **Add the results together:**
\[
81 + 108 + 16 = 205
\]
**Therefore, the value of the expression is 205.**
**Answer:** D) 205
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Simplify this solution Extra Insights
Let's plug the values of \( x \) and \( y \) into the expression \( x^{2}+3 x y+y^{2} \). First, calculate \( x^{2} \): \( x^{2} = 9^{2} = 81 \). Next, calculate \( 3xy \): \( 3xy = 3 \times 9 \times 4 = 108 \). Then, calculate \( y^{2} \): \( y^{2} = 4^{2} = 16 \). Now, combine these values: \( 81 + 108 + 16 = 205 \). Therefore, the correct answer is **D 205**.
