To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the distributive property, you will distribute each term in the first parentheses across each term in the second parentheses.
Here’s how it works step-by-step:
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Distribute \(3x\) to both \(x\) and \(-4\):
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)
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Distribute \(-1\) to both \(x\) and \(-4\):
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)
Now, combine all the results:
\[ 3x^2 - 12x - x + 4 \]
Next, combine the like terms (\(-12x\) and \(-x\)):
\[ 3x^2 - 13x + 4 \]
So, the rewritten expression is:
\[ 3x^2 - 13x + 4 \]