To rewrite \((3x - 1)(x - 4)\) using the distributive property, we apply the distributive law, which involves multiplying each term in the first parentheses by each term in the second parentheses.
Here’s the step-by-step breakdown:
-
Distribute \(3x\) to both terms in the second parentheses: \[ 3x \cdot x = 3x^2 \] \[ 3x \cdot (-4) = -12x \]
-
Distribute \(-1\) to both terms in the second parentheses: \[ -1 \cdot x = -x \] \[ -1 \cdot (-4) = 4 \]
-
Now, combine all the results: \[ 3x^2 - 12x - x + 4 \]
-
Finally, combine like terms: \[ 3x^2 - 13x + 4 \]
So, the expression \((3x - 1)(x - 4)\) rewritten using the distributive property is: \[ 3x^2 - 13x + 4 \]
1 answer