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3. Expand \( (2 x+1)(3 x-4) \)

Ask by Kirk Moreno. in Fiji
Nov 02,2024

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Answer

\( 6x^{2}-5x-4 \)

Solution

Expand the expression \( (2x+1)(3x-4) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(2x+1\right)\left(3x-4\right)\) - step1: Apply the distributive property: \(2x\times 3x-2x\times 4+1\times 3x-1\times 4\) - step2: Multiply the terms: \(6x^{2}-8x+3x-4\) - step3: Add the terms: \(6x^{2}-5x-4\) Expanding the expression \( (2x+1)(3x-4) \) gives \( 6x^{2}-5x-4 \).

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Bonus Knowledge

To expand \( (2 x+1)(3 x-4) \), we apply the distributive property (also known as the FOIL method for binomials). Multiplying each term in the first parenthesis by each term in the second gives us: 1. \( 2x \cdot 3x = 6x^2 \) 2. \( 2x \cdot (-4) = -8x \) 3. \( 1 \cdot 3x = 3x \) 4. \( 1 \cdot (-4) = -4 \) Now, we combine like terms: \[ 6x^2 + (-8x + 3x) - 4 = 6x^2 - 5x - 4 \] Thus, the expanded form is \( 6x^2 - 5x - 4 \).

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