Question
Simplify the following difference of polynomials eompletely, \[ \left(A^{2}+t^{2}\right)-\left(-15 B^{2}+2 A t-8 t^{2}\right) \]
Ask by Carrillo Cook. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified difference of polynomials is \( A^{2} + 9t^{2} + 15B^{2} - 2At \).
Solution
Calculate or simplify the expression \( (A^2+t^2)-(-15B^2+2At-8t^2) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(A^{2}+t^{2}\right)-\left(-15B^{2}+2At-8t^{2}\right)\)
- step1: Remove the parentheses:
\(A^{2}+t^{2}-\left(-15B^{2}+2At-8t^{2}\right)\)
- step2: Remove the parentheses:
\(A^{2}+t^{2}+15B^{2}-2At+8t^{2}\)
- step3: Add the terms:
\(A^{2}+9t^{2}+15B^{2}-2At\)
The simplified difference of polynomials is \(A^{2}+9t^{2}+15B^{2}-2At\).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To simplify the given expression, we start by distributing the negative sign across the second polynomial: \[ \left(A^{2} + t^{2}\right) - \left(-15 B^{2} + 2 A t - 8 t^{2}\right) = A^{2} + t^{2} + 15 B^{2} - 2 A t + 8 t^{2} \] Next, we combine like terms: 1. The \( t^{2} \) terms: \( t^{2} + 8 t^{2} = 9 t^{2} \) 2. The other terms stay as they are: \( A^{2}, 15 B^{2}, -2 A t \) Now we can write the simplified expression: \[ A^{2} + 15 B^{2} - 2 A t + 9 t^{2} \] So, the final simplified expression is: \[ A^{2} + 15 B^{2} - 2 A t + 9 t^{2} \]
