According to the Distributive Property, which is a way to rewrite the algebraic expression (3x - 1) (x - 4)

1 answer

To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the Distributive Property, you will need to distribute each term in the first parentheses by each term in the second parentheses.

Here’s how it’s done step by step:

  1. Distribute \(3x\) to both \(x\) and \(-4\): \[ 3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x \]

  2. Distribute \(-1\) to both \(x\) and \(-4\): \[ -1 \cdot x + (-1) \cdot (-4) = -x + 4 \]

  3. Now, combine all the terms: \[ 3x^2 - 12x - x + 4 \]

  4. Combine like terms \(-12x\) and \(-x\): \[ -12x - x = -13x \]

Therefore, the expression \((3x - 1)(x - 4)\) can be rewritten as: \[ 3x^2 - 13x + 4 \]

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