Question
Simplify the following difference of polynomials completely. \[ \left(s^{2}+t^{2}\right)-\left(-15 s^{2}+2 s t-8 t\right. \]
Ask by Bob Sandoval. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(16s^{2} + t^{2} - 2st + 8t\).
Solution
\[
\textbf{Step 1: Distribute the subtraction sign}
\]
Starting with the expression:
\[
\left(s^{2}+t^{2}\right)-\left(-15 s^{2}+2 s t-8 t\right)
\]
we distribute the minus sign across the second set of terms:
\[
= s^{2} + t^{2} + 15s^{2} - 2st + 8t
\]
\[
\textbf{Step 2: Combine like terms}
\]
Combine the \( s^2 \) terms:
\[
s^{2} + 15s^{2} = 16s^{2}
\]
There are no like terms for \( t^{2} \), \( -2st \), or \( 8t \). Thus, the simplified expression is:
\[
16s^{2} + t^{2} - 2st + 8t
\]
\[
\boxed{16s^{2} + t^{2} - 2st + 8t}
\]
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Simplify this solution Bonus Knowledge
To simplify the expression \(\left(s^{2}+t^{2}\right)-\left(-15 s^{2}+2 s t-8 t\right)\), start by distributing the negative sign into the second polynomial: \[ s^{2} + t^{2} + 15 s^{2} - 2 s t + 8 t \] Now, combine the like terms: \[ (s^{2} + 15 s^{2}) + t^{2} - 2 s t + 8 t \] This leads to: \[ 16 s^{2} + t^{2} - 2 s t + 8 t \] Therefore, the simplified expression is: \[ 16 s^{2} + t^{2} - 2 s t + 8 t \]
