Question
Find the product. Simplify your answer. \( (4 s-2)(2 s-3) \)
Ask by Whittaker Ramos. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 8s^2 - 16s + 6 \)
Solution
To find the product of the binomials \( (4s - 2)(2s - 3) \) and simplify the expression, follow these steps:
1. **Apply the Distributive Property (FOIL Method):**
Multiply each term in the first binomial by each term in the second binomial.
\[
\begin{align*}
(4s - 2)(2s - 3) &= 4s \cdot 2s + 4s \cdot (-3) + (-2) \cdot 2s + (-2) \cdot (-3) \\
&= 8s^2 - 12s - 4s + 6
\end{align*}
\]
2. **Combine Like Terms:**
Add the coefficients of the \( s \) terms.
\[
8s^2 - 12s - 4s + 6 = 8s^2 - 16s + 6
\]
3. **Final Simplified Expression:**
\[
(4s - 2)(2s - 3) = 8s^2 - 16s + 6
\]
**Answer:** \( 8s^2 - 16s + 6 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the product of \( (4s - 2)(2s - 3) \), you can use the distributive property, also known as the FOIL method for binomials. First, multiply: - The first terms: \( 4s \cdot 2s = 8s^2 \) - The outer terms: \( 4s \cdot (-3) = -12s \) - The inner terms: \( -2 \cdot 2s = -4s \) - The last terms: \( -2 \cdot (-3) = 6 \) Now combine these results: \[ 8s^2 - 12s - 4s + 6 = 8s^2 - 16s + 6 \] Thus, the simplified product is: \[ 8s^2 - 16s + 6 \]
