Question
Find the product of the polynomials: \( (5y - 2)(y + 6) \)
Ask by Guzman Bryant. in South Africa
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product of the polynomials \( (5y - 2)(y + 6) \) is \( 5y^2 + 28y - 12 \).
Solution
To find the product of the polynomials \( (5y - 2)(y + 6) \), 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.
\[
5y \times y = 5y^2
\]
2. **Outer Terms:** Multiply the outer terms.
\[
5y \times 6 = 30y
\]
3. **Inner Terms:** Multiply the inner terms.
\[
-2 \times y = -2y
\]
4. **Last Terms:** Multiply the last terms in each binomial.
\[
-2 \times 6 = -12
\]
**Combine All the Terms:**
\[
5y^2 + 30y - 2y - 12
\]
**Simplify by Combining Like Terms:**
\[
5y^2 + (30y - 2y) - 12 = 5y^2 + 28y - 12
\]
**Final Answer:**
\[
5y^2 + 28y - 12
\]
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Simplify this solution Bonus Knowledge
To find the product of the polynomials \( (5y - 2)(y + 6) \), we can use the distributive property, also known as the FOIL method for binomials. 1. Multiply the first terms: \( 5y \cdot y = 5y^2 \) 2. Multiply the outer terms: \( 5y \cdot 6 = 30y \) 3. Multiply the inner terms: \( -2 \cdot y = -2y \) 4. Multiply the last terms: \( -2 \cdot 6 = -12 \) Now, we combine all these results together: \[ 5y^2 + 30y - 2y - 12 \] Combine like terms: \[ 5y^2 + (30y - 2y) - 12 = 5y^2 + 28y - 12 \] So the product of the polynomials \( (5y - 2)(y + 6) \) is: \[ \boxed{5y^2 + 28y - 12} \]
