Question
Multiply the polynomials: \( (2x + 3)(3x + 4) \)
Ask by Salazar Luna. in India
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Multiply the polynomials \( (2x + 3)(3x + 4) \) to get \( 6x^2 + 17x + 12 \).
Solution
To multiply the polynomials \( (2x + 3)(3x + 4) \), you can use the distributive property (also known as the FOIL method for binomials):
1. **First terms:** \( 2x \times 3x = 6x^2 \)
2. **Outer terms:** \( 2x \times 4 = 8x \)
3. **Inner terms:** \( 3 \times 3x = 9x \)
4. **Last terms:** \( 3 \times 4 = 12 \)
Now, combine all these results:
\[
6x^2 + 8x + 9x + 12
\]
Combine the like terms (\(8x\) and \(9x\)):
\[
6x^2 + 17x + 12
\]
**Final Answer:**
\[
6x^2 + 17x + 12
\]
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Simplify this solution Bonus Knowledge
To multiply the polynomials \( (2x + 3)(3x + 4) \), we use the distributive property (also known as the FOIL method for binomials). First, multiply the first terms: \[ 2x \cdot 3x = 6x^2. \] Next, multiply the outer terms: \[ 2x \cdot 4 = 8x. \] Then, multiply the inner terms: \[ 3 \cdot 3x = 9x. \] Finally, multiply the last terms: \[ 3 \cdot 4 = 12. \] Now, combine all the like terms: \[ 6x^2 + 8x + 9x + 12 = 6x^2 + 17x + 12. \] So, the final result is: \[ 6x^2 + 17x + 12. \]
