Question
23. \( \frac{4 t+4}{t-3} \cdot\left(t^{2}-t-6\right) \)
Ask by Higgins Nichols. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of the expression is \( 4t^{2}+12t+8 \).
Solution
Calculate or simplify the expression \( (4t+4)/(t-3) * (t^2-t-6) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(4t+4\right)}{\left(t-3\right)}\times \left(t^{2}-t-6\right)\)
- step1: Remove the parentheses:
\(\frac{4t+4}{t-3}\times \left(t^{2}-t-6\right)\)
- step2: Rewrite the expression:
\(\frac{4t+4}{t-3}\times \left(t-3\right)\left(t+2\right)\)
- step3: Reduce the fraction:
\(\left(4t+4\right)\left(t+2\right)\)
- step4: Apply the distributive property:
\(4t\times t+4t\times 2+4t+4\times 2\)
- step5: Multiply the terms:
\(4t^{2}+8t+4t+8\)
- step6: Add the terms:
\(4t^{2}+12t+8\)
The simplified form of the expression \( \frac{4t+4}{t-3} \cdot\left(t^{2}-t-6\right) \) is \( 4t^{2}+12t+8 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
Let's break it down! The expression \( t^{2}-t-6 \) can be factored into \( (t-3)(t+2) \). Now we can rewrite the original expression: \[ \frac{4(t+1)}{t-3} \cdot (t-3)(t+2) \] Observe that the \( (t-3) \) in the numerator and denominator cancels out, simplifying the expression to: \[ 4(t+1)(t+2) \] Now, we can distribute: \[ 4 \left( t^2 + 3t + 2 \right) \] Finally, multiplying through by 4 gives us: \[ 4t^2 + 12t + 8 \] And that's the simplified result!
