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\left(-2x+4x^{3}+8\right)\left(-\frac{1}{2}\right)x^{2}
To find the opposite of 2x-4x^{3}-8, find the opposite of each term.
\left(x-2x^{3}-4\right)x^{2}
Use the distributive property to multiply -2x+4x^{3}+8 by -\frac{1}{2}.
x^{3}-2x^{5}-4x^{2}
Use the distributive property to multiply x-2x^{3}-4 by x^{2}.
\left(-2x+4x^{3}+8\right)\left(-\frac{1}{2}\right)x^{2}
To find the opposite of 2x-4x^{3}-8, find the opposite of each term.
\left(x-2x^{3}-4\right)x^{2}
Use the distributive property to multiply -2x+4x^{3}+8 by -\frac{1}{2}.
x^{3}-2x^{5}-4x^{2}
Use the distributive property to multiply x-2x^{3}-4 by x^{2}.