Minding the Signs

When the multiplier is negative, its minus sign is part of every product. In $-2x\left(x+5\right)$, the multiplier is $-2x$, so each product is negative. $-2xx = -2x^{2}$ and $-2x\cdot 5 = -10x$. The answer is $-2x^{2}-10x$.

When there are negative terms inside as well, decide the sign of each product separately, using the rules for multiplying signed numbers. In $-2x\left(x-5\right)$, the first product is $-2x^{2}$. The second product is $-2x$ times $-5$, which is $10x$, because two negatives multiply to a positive. The result is $-2x^{2}+10x$.

Write the sign of each product as you distribute. A negative multiplier changes the sign of every term inside the parentheses. A positive term gives a negative product, and a negative term gives a positive product.