![To simplify the expression \((2x - 3)(4x + 1)\), we can use the distributive property (also known as the FOIL method for binomials):
1. First, multiply the first terms: \(2x \cdot 4x = 8x^2\)
2. Next, multiply the outer terms: \(2x \cdot 1 = 2x\)
3. Then, multiply the inner terms: \(-3 \cdot 4x = -12x\)
4. Finally, multiply the last terms: \(-3 \cdot 1 = -3\)
Now, combine all the results:
\[
8x^2 + 2x - 12x - 3 = 8x^2 - 10x - 3
\]
Thus, the simplified expression is:
**D. \(8x^2 - 10x - 3\)*](https://theinternetioimages-f2htc2ggcrath6d7.z01.azurefd.net/$web/askai/43780f62-fb65-4e65-ada7-33cc2c12530c.webp)
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Question: 12. Simplify: (2x − 3)(4x + 1) = A. 8x2 − 14x − 3 B. 8x2 + 14x − 3 C. 8x2 + 10x − 3 D. 8x2 − 10x − 3
To simplify the expression \((2x - 3)(4x + 1)\), we can use the distributive property (also known as the FOIL method for binomials): 1. **First terms**: \(2x \cdot 4x = 8x^2\) 2. **Outer terms**: \(2x \cdot 1 = 2x\) 3. **Inner terms**: \(-3 \cdot 4x = -12x\) 4. **Last terms**: \(-3 \cdot 1 = -3\) Now combine these results: \[8x^2 + 2x - 12x - 3\] Combine the like terms (\(2x - 12x\)): \[8x^2 - 10x - 3\] So, the simplified expression is: \[8x^2 - 10x - 3\] Therefore, the correct answer is: D. \(8x^2 - 10x - 3\)
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