Question
\( 6 . \quad ( 3 x ^ { 2 } + 6 x - 5 ) ( - 3 x ) \)
Ask by Klein Curry. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression simplifies to \( -9x^3 - 18x^2 + 15x \).
Solution
Calculate or simplify the expression \( (3x^2 + 6x - 5) * (-3x) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(3x^{2}+6x-5\right)\left(-3x\right)\)
- step1: Multiply the terms:
\(-3x\left(3x^{2}+6x-5\right)\)
- step2: Apply the distributive property:
\(-3x\times 3x^{2}-3x\times 6x-\left(-3x\times 5\right)\)
- step3: Multiply the terms:
\(-9x^{3}-18x^{2}-\left(-15x\right)\)
- step4: Remove the parentheses:
\(-9x^{3}-18x^{2}+15x\)
The expression \( (3x^2 + 6x - 5) \times (-3x) \) simplifies to \( -9x^3 - 18x^2 + 15x \).
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Simplify this solution Beyond the Answer
To dive into this expression, let's expand it! When you multiply \( -3x \) by each term inside the parentheses, it results in: - \( -3x \cdot 3x^2 = -9x^3 \) - \( -3x \cdot 6x = -18x^2 \) - \( -3x \cdot (-5) = 15x \) So, combining all these results, the final expanded expression becomes: \[ -9x^3 - 18x^2 + 15x \] Now, moving on to analyzing this expression, you could be curious about its roots or behavior! To explore, you could set it equal to zero and use factoring or the quadratic formula for roots, turning this equation into a quest for x-values that satisfy the polynomial equation. It's like a mathematical treasure hunt!
