To apply the distributive property to rewrite the expression \((2x-2)(x-6)\), we can distribute each term in the first parentheses across each term in the second parentheses.
Here’s how you do it step by step:
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Distribute \(2x\) to both terms in \((x - 6)\):
- \(2x \cdot x = 2x^2\)
- \(2x \cdot -6 = -12x\)
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Distribute \(-2\) to both terms in \((x - 6)\):
- \(-2 \cdot x = -2x\)
- \(-2 \cdot -6 = 12\)
Now, combine all the results: \[ 2x^2 - 12x - 2x + 12 \]
Next, combine the like terms \(-12x\) and \(-2x\): \[ 2x^2 - 14x + 12 \]
So, the expression \((2x-2)(x-6)\) rewritten using the distributive property is: \[ 2x^2 - 14x + 12 \]