To simplify the expression \(-4(x^2 + 1) + 3x^2\), follow these steps:
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Distribute \(-4\) to both terms inside the parentheses: \[ -4(x^2) - 4(1) + 3x^2 = -4x^2 - 4 + 3x^2 \]
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Combine like terms (\(-4x^2\) and \(3x^2\)): \[ (-4x^2 + 3x^2) - 4 = -1x^2 - 4 \]
Thus, the simplified expression is: \[ -x^2 - 4 \]