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-\left(1-12x+48x^{2}-64x^{3}\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(1-4x\right)^{3}.
-1+12x-48x^{2}+64x^{3}
To find the opposite of 1-12x+48x^{2}-64x^{3}, find the opposite of each term.
-\left(1-12x+48x^{2}-64x^{3}\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(1-4x\right)^{3}.
-1+12x-48x^{2}+64x^{3}
To find the opposite of 1-12x+48x^{2}-64x^{3}, find the opposite of each term.