Question
What is the product? \( 6\left(x^{2}-1\right) \cdot \frac{6 x-1}{6(x+1)} \)
Ask by Brooks Henry. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The product is \(6x^{2}-7x+1\).
Solution
Calculate or simplify the expression \( 6(x^2-1) * (6x-1)/(6(x+1)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{6\left(x^{2}-1\right)\left(6x-1\right)}{\left(6\left(x+1\right)\right)}\)
- step1: Remove the parentheses:
\(\frac{6\left(x^{2}-1\right)\left(6x-1\right)}{6\left(x+1\right)}\)
- step2: Reduce the fraction:
\(\frac{\left(x^{2}-1\right)\left(6x-1\right)}{x+1}\)
- step3: Factor the expression:
\(\frac{\left(x+1\right)\left(x-1\right)\left(6x-1\right)}{x+1}\)
- step4: Reduce the fraction:
\(\left(x-1\right)\left(6x-1\right)\)
- step5: Apply the distributive property:
\(x\times 6x-x\times 1-6x-\left(-1\right)\)
- step6: Multiply the terms:
\(6x^{2}-x-6x-\left(-1\right)\)
- step7: Remove the parentheses:
\(6x^{2}-x-6x+1\)
- step8: Subtract the terms:
\(6x^{2}-7x+1\)
The product of \(6\left(x^{2}-1\right) \cdot \frac{6 x-1}{6(x+1)}\) is \(6x^{2}-7x+1\).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To simplify the expression \( 6\left(x^{2}-1\right) \cdot \frac{6 x-1}{6(x+1)} \), we start by recognizing that \( x^2 - 1 \) can be factored. The factored form is \( (x-1)(x+1) \). Now, substituting that in, we have: \[ 6 \cdot (x-1)(x+1) \cdot \frac{6x-1}{6(x+1)} \] Notice that \( (x+1) \) in the numerator and denominator cancels out when \( x \neq -1\). Therefore, the product simplifies to: \[ 6(x-1) \cdot \frac{6x-1}{6} \] The \( 6 \) in the numerator and denominator cancels, giving: \[ (x-1)(6x-1) \] Now, distributing this product results in: \[ 6x^2 - x - 6 + 1 \] Combining terms yields: \[ 6x^2 - 7x + 1 \] Thus, the simplified product is: \[ 6x^2 - 7x + 1 \]
