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2002 AMC 10B Problem 4

Problem 4 of 25EasierAlgebraArithmetic

What is the value of (3x−2)(4x+1)−(3x−2)4x+1 \begin{aligned} &(3x - 2)(4x + 1) \\ &\quad {}- (3x - 2)4x + 1 \end{aligned} when x=4?x = 4?

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Solution

Factoring 3x−23x-2 from the first two terms, (3x−2)[(4x+1)−4x]+1=(3x−2)(1)+1=3x−1. \begin{aligned} &(3x - 2)\big[(4x + 1) - 4x\big] + 1 \\ &= (3x - 2)(1) + 1 \\ &= 3x - 1. \end{aligned} At x=4,x = 4, this equals 3⋅4−1=11.3\cdot4 - 1 = 11. Thus, the correct answer is D.
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Tagged: distributive property · factoring

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