To evaluate the expression \(-6 \cdot (xz^2 + x + y)\) for \(x = 6\), \(y = -13\), and \(z = 1\), we will first substitute the values of \(x\), \(y\), and \(z\) into the expression.
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Calculate \(z^2\): \[ z^2 = 1^2 = 1 \]
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Calculate \(xz^2\): \[ xz^2 = 6 \cdot 1 = 6 \]
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Now substitute \(x\) and \(y\) into the expression \(xz^2 + x + y\): \[ xz^2 + x + y = 6 + 6 + (-13) \] \[ = 6 + 6 - 13 = 12 - 13 = -1 \]
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Now substitute back into the original expression: \[ -6 \cdot (xz^2 + x + y) = -6 \cdot (-1) = 6 \]
Thus, the simplified answer is: \[ \boxed{6} \]
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