Coleman Frank
03/14/2024 · Middle School
Find the product: \( (7 x+5 y)(5 x-4 y) \) A. \( 35 x^{2}+20 y^{2} \) B. \( 56 x^{2}-17 x y-3 y^{2} \) C. \( 35 x^{2}+53 x y+20 y^{2} \) D. \( 35 x^{2}-3 x y-20 y^{2} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the product \( (7x + 5y)(5x - 4y) \), we can use the distributive property (also known as the FOIL method for binomials).
1. **First**: Multiply the first terms:
\[
7x \cdot 5x = 35x^2
\]
2. **Outer**: Multiply the outer terms:
\[
7x \cdot (-4y) = -28xy
\]
3. **Inner**: Multiply the inner terms:
\[
5y \cdot 5x = 25xy
\]
4. **Last**: Multiply the last terms:
\[
5y \cdot (-4y) = -20y^2
\]
Now, we combine all these results:
\[
35x^2 - 28xy + 25xy - 20y^2
\]
Next, we combine the like terms:
\[
-28xy + 25xy = -3xy
\]
Thus, the final expression is:
\[
35x^2 - 3xy - 20y^2
\]
Now, we can compare this result with the provided options:
- A. \( 35 x^{2}+20 y^{2} \)
- B. \( 56 x^{2}-17 x y-3 y^{2} \)
- C. \( 35 x^{2}+53 x y+20 y^{2} \)
- D. \( 35 x^{2}-3 x y-20 y^{2} \)
The correct answer is:
\[
\boxed{D}
\]
Quick Answer
The correct answer is D. \( 35 x^{2}-3 x y-20 y^{2} \)
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