Question
8. Compute the following product. \[(5 x-2)(x+1)\]
Ask by Huang Vaughan. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product is \(5x^2 + 3x - 2\).
Solution
To compute the product \((5x - 2)(x + 1)\), we'll use the distributive property (also known as the FOIL method for binomials).
**Step-by-Step Expansion:**
1. **First Terms:** Multiply the first terms in each binomial:
\[
5x \cdot x = 5x^2
\]
2. **Outer Terms:** Multiply the outer terms:
\[
5x \cdot 1 = 5x
\]
3. **Inner Terms:** Multiply the inner terms:
\[
-2 \cdot x = -2x
\]
4. **Last Terms:** Multiply the last terms in each binomial:
\[
-2 \cdot 1 = -2
\]
**Combine All the Products:**
\[
5x^2 + 5x - 2x - 2
\]
**Simplify Like Terms:**
\[
5x^2 + 3x - 2
\]
**Final Answer:**
\[
5x^2 + 3x - 2
\]
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Simplify this solution Extra Insights
To compute the product \((5x - 2)(x + 1)\), we can use the distributive property (also known as the FOIL method for binomials). 1. First, distribute \(5x\) to both terms in the second binomial: \[ 5x \cdot x + 5x \cdot 1 = 5x^2 + 5x \] 2. Next, distribute \(-2\) to both terms in the second binomial: \[ -2 \cdot x - 2 \cdot 1 = -2x - 2 \] 3. Now, combine all the terms: \[ 5x^2 + 5x - 2x - 2 \] 4. Combine like terms: \[ 5x^2 + (5x - 2x) - 2 = 5x^2 + 3x - 2 \] So, the final product is: \[ \boxed{5x^2 + 3x - 2} \]
