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x-5x\left(x^{2}-3x\right)-x^{2}+2x-3+5x^{3}
To find the opposite of x^{2}-2x+3, find the opposite of each term.
x-5x^{3}+15x^{2}-x^{2}+2x-3+5x^{3}
Use the distributive property to multiply -5x by x^{2}-3x.
x-5x^{3}+14x^{2}+2x-3+5x^{3}
Combine 15x^{2} and -x^{2} to get 14x^{2}.
3x-5x^{3}+14x^{2}-3+5x^{3}
Combine x and 2x to get 3x.
3x+14x^{2}-3
Combine -5x^{3} and 5x^{3} to get 0.
x-5x\left(x^{2}-3x\right)-x^{2}+2x-3+5x^{3}
To find the opposite of x^{2}-2x+3, find the opposite of each term.
x-5x^{3}+15x^{2}-x^{2}+2x-3+5x^{3}
Use the distributive property to multiply -5x by x^{2}-3x.
x-5x^{3}+14x^{2}+2x-3+5x^{3}
Combine 15x^{2} and -x^{2} to get 14x^{2}.
3x-5x^{3}+14x^{2}-3+5x^{3}
Combine x and 2x to get 3x.
3x+14x^{2}-3
Combine -5x^{3} and 5x^{3} to get 0.