Question
Find the product: \( (8 n-3)(5 n+7) \) \( 40 n^{2}-21 \) \( 13 n^{2}+17 n+4 \) \( 40 n^{2}-41 n-21 \) \( 40 n^{2}+41 n-21 \)
Ask by Lynch Rowe. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product is \( 40n^{2} + 41n - 21 \).
Solution
To find the product of the binomials \( (8n - 3)(5n + 7) \), we can use the distributive property (also known as the FOIL method for binomials):
\[
(8n - 3)(5n + 7) = 8n \cdot 5n + 8n \cdot 7 - 3 \cdot 5n - 3 \cdot 7
\]
Let's calculate each term step by step:
1. **First Terms:** \( 8n \cdot 5n = 40n^2 \)
2. **Outer Terms:** \( 8n \cdot 7 = 56n \)
3. **Inner Terms:** \( -3 \cdot 5n = -15n \)
4. **Last Terms:** \( -3 \cdot 7 = -21 \)
Now, combine all the terms:
\[
40n^2 + 56n - 15n - 21
\]
Combine like terms:
\[
40n^2 + (56n - 15n) - 21 = 40n^2 + 41n - 21
\]
**Final Answer:**
\[
40n^{2} + 41n - 21
\]
This corresponds to the fourth option:
\[
40 n^{2}+41 n-21
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the product \( (8n - 3)(5n + 7) \), we can use the distributive property (also known as the FOIL method for binomials). 1. Multiply the first terms: \( 8n \cdot 5n = 40n^2 \) 2. Multiply the outer terms: \( 8n \cdot 7 = 56n \) 3. Multiply the inner terms: \( -3 \cdot 5n = -15n \) 4. Multiply the last terms: \( -3 \cdot 7 = -21 \) Now, combine these results: - The \( n^2 \) term: \( 40n^2 \) - The \( n \) terms: \( 56n - 15n = 41n \) - The constant term: \( -21 \) So the final expression is: \[ 40n^2 + 41n - 21 \] Thus, the product is \( 40n^2 + 41n - 21 \).
