Question
Scan for seveled Pracsice in \( 76-26 \), combine like terms to simplify each expression. 18. \( 2.1 x^{2}+3-0.5 x^{2}-1 \) \( =\left(x^{2}-\square x^{2}\right)+(3-1) \) \[ =\square x^{2}+\square \]
Ask by Donnelly Coles. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 1.6x^{2} + 2 \)
Solution
Let's simplify the expression step by step.
1. **Identify the expression**:
The expression given is \( 2.1 x^{2} + 3 - 0.5 x^{2} - 1 \).
2. **Combine like terms**:
- The like terms for \( x^{2} \) are \( 2.1 x^{2} \) and \( -0.5 x^{2} \).
- The constant terms are \( 3 \) and \( -1 \).
3. **Calculate the coefficients of \( x^{2} \)**:
\[
2.1 - 0.5 = 1.6
\]
So, the combined term for \( x^{2} \) is \( 1.6 x^{2} \).
4. **Calculate the constant terms**:
\[
3 - 1 = 2
\]
So, the combined constant term is \( 2 \).
5. **Final expression**:
Putting it all together, we have:
\[
1.6 x^{2} + 2
\]
Now, let's fill in the squares in your original format:
\[
= \left(x^{2} - 0.5 x^{2}\right) + (3 - 1)
\]
\[
= 1.6 x^{2} + 2
\]
Thus, the final answer is:
\[
= 1.6 x^{2} + 2
\]
In summary:
- The coefficient of \( x^{2} \) is \( 1.6 \).
- The constant term is \( 2 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
Let's break down the expression \( 2.1 x^{2} + 3 - 0.5 x^{2} - 1 \) step by step! First, combine the \( x^{2} \) terms: \( 2.1 x^{2} - 0.5 x^{2} = 1.6 x^{2} \). Now, combine the constant terms: \( 3 - 1 = 2 \). So your simplified expression is \( 1.6 x^{2} + 2 \). Now, let's fill in the blanks from your expression: \[ = \left(x^{2} - 0.5 x^{2}\right) + (3 - 1) \] \[ = 1.6 x^{2} + 2 \] Great job simplifying that expression!
