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$Simplify $ (2 x+3)(x-4) $ A. $ \quad 2 x^{2}-8 $ B. $ 2 x^{2}+7 x-12 $ C. $ 2 x^{2}-11 x-12 $ D. $ 2 x^{2}-5 x-12 $$

Simplify $ (2 x+3)(x-4) $ A. $ \quad 2 x^{2}-8 $ B. $ 2 x^{2}+7 x-12 $ C. $ 2 x^{2}-11 x-12 $ D. $ 2 x^{2}-5 x-12 $

Ask by Gibbs Medina.

Nov 10,2024 12:18

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Tutor-Verified Answer

Answer

$ 2x^{2}-5x-12 $. Therefore, the correct answer is D. $ 2x^{2}-5x-12 $.

Solution

Calculate or simplify the expression $ (2*x+3)*(x-4) $. Simplify the expression by following steps: - step0: Solution: $\left(2x+3\right)\left(x-4\right)$ - step1: Apply the distributive property: $2x\times x-2x\times 4+3x-3\times 4$ - step2: Multiply the terms: $2x^{2}-8x+3x-12$ - step3: Add the terms: $2x^{2}-5x-12$ The simplified form of $ (2x+3)(x-4) $ is $ 2x^{2}-5x-12 $. Therefore, the correct option is D. $ 2x^{2}-5x-12 $.

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Bonus Knowledge

To simplify $ (2 x+3)(x-4) $, we can use the distributive property (or the FOIL method). 1. Multiply the first terms: $ 2x \cdot x = 2x^2 $. 2. Multiply the outer terms: $ 2x \cdot -4 = -8x $. 3. Multiply the inner terms: $ 3 \cdot x = 3x $. 4. Multiply the last terms: $ 3 \cdot -4 = -12 $. Now, combine the like terms: \[ 2x^2 - 8x + 3x - 12 = 2x^2 - 5x - 12 \] So, the simplified expression is $ 2x^2 - 5x - 12 $, which corresponds to option D. **Final Answer: D. $ 2 x^{2}-5 x-12 $**