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Multiply the polynomials: \( (2x + 3)(3x + 4) \)

Ask by Salazar Luna. in India
Jan 22,2025

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Multiply the polynomials \( (2x + 3)(3x + 4) \) to get \( 6x^2 + 17x + 12 \).

Solución

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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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: \[ 6x^2 + 17x + 12. \]

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