Question
Factor \( 2 t^{2}+15 t z^{3}-6 t-45 z^{3} \) completely.
Ask by Savage Phillips. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The expression factors to \((15z^{3}+2t)(t-3)\).
Solution
Factor the expression \( 2t^{2}+15tz^{3}-6t-45z^{3} \).
Factor the expression by following steps:
- step0: Factor:
\(2t^{2}+15tz^{3}-6t-45z^{3}\)
- step1: Rewrite the expression:
\(15z^{3}t-45z^{3}+2t^{2}-6t\)
- step2: Factor the expression:
\(15z^{3}\left(t-3\right)+2t\left(t-3\right)\)
- step3: Factor the expression:
\(\left(15z^{3}+2t\right)\left(t-3\right)\)
The factored form of the expression \(2t^{2}+15tz^{3}-6t-45z^{3}\) is \((15z^{3}+2t)(t-3)\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To factor the expression \( 2t^{2} + 15tz^{3} - 6t - 45z^{3} \), we can start by rearranging it: \[ 2t^{2} - 6t + 15tz^{3} - 45z^{3} \] Now, we can group the terms: \[ (2t^{2} - 6t) + (15tz^{3} - 45z^{3}) \] Factoring out the common factors from each group: \[ 2t(t - 3) + 15z^{3}(t - 3) \] Now, we notice that both terms share a common factor of \( (t - 3) \): \[ (t - 3)(2t + 15z^{3}) \] This gives us the completely factored form: \[ \boxed{(t - 3)(2t + 15z^{3})} \]
