Question
Select the simplified form of this expression \[ \frac{1}{7} x^{2}(x-7) \]
Ask by Franklin Clark. in the United States
Mar 05,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( \frac{1}{7}x^{3} - x^{2} \).
Solution
Calculate or simplify the expression \( \frac{1}{7}x^{2}(x-7) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{1}{7}x^{2}\left(x-7\right)\)
- step1: Rewrite the expression:
\(7^{-1}\left(x-7\right)x^{2}\)
- step2: Multiply the expression:
\(\frac{1}{7}\left(x-7\right)x^{2}\)
- step3: Rearrange the terms:
\(\left(x-7\right)\times \frac{1}{7}x^{2}\)
- step4: Apply the distributive property:
\(x\times \frac{1}{7}x^{2}-7\times \frac{1}{7}x^{2}\)
- step5: Multiply the terms:
\(\frac{1}{7}x^{3}-x^{2}\)
The simplified form of the expression \(\frac{1}{7} x^{2}(x-7)\) is \(\frac{1}{7}x^{3}-x^{2}\).
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Simplify this solution The Deep Dive
To simplify the expression \(\frac{1}{7} x^{2}(x-7)\), we can distribute \(x^{2}\) to both terms inside the parentheses. This gives us: \[ \frac{1}{7} (x^{3} - 7x^{2}). \] Now, we can apply the \(\frac{1}{7}\) to both terms: \[ \frac{1}{7} x^{3} - \frac{7}{7} x^{2} = \frac{1}{7} x^{3} - x^{2}. \] So, the simplified form of the expression is: \[ \frac{1}{7} x^{3} - x^{2}. \]
