To simplify the expression \((-4 \times 2x) + (-4 \times 5)\), we can first perform the multiplications separately:
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For \(-4 \times 2x\): \[ -4 \times 2x = -8x \]
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For \(-4 \times 5\): \[ -4 \times 5 = -20 \]
Now, we can combine these results: \[ -8x + (-20) = -8x - 20 \]
Thus, the simplified expression is: \[ -8x - 20 \]