Question
\( 1 \leftarrow \quad \) Use the FOIL method to find the product. \[ (v+9)(v-7) \]
Ask by Hodges Henry. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( (v + 9)(v - 7) = v^2 + 2v - 63 \)
Solution
1. **First:** Multiply the first terms of each binomial:
\[
v \times v = v^2.
\]
2. **Outer:** Multiply the outer terms:
\[
v \times (-7) = -7v.
\]
3. **Inner:** Multiply the inner terms:
\[
9 \times v = 9v.
\]
4. **Last:** Multiply the last terms of each binomial:
\[
9 \times (-7) = -63.
\]
5. **Combine like terms:**
\[
v^2 - 7v + 9v - 63 = v^2 + 2v - 63.
\]
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Simplify this solution Extra Insights
To find the product of \( (v+9)(v-7) \) using the FOIL method, we simply multiply the terms: First: \( v \times v = v^2 \) Outer: \( v \times -7 = -7v \) Inner: \( 9 \times v = 9v \) Last: \( 9 \times -7 = -63 \) Now, combine the results: \[ v^2 - 7v + 9v - 63 \] Combine like terms: \[ v^2 + 2v - 63 \] So, the product is \( v^2 + 2v - 63 \).
