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6x^{3}-4x^{2}-2x-12+9x^{2}-\left(4x^{3}-9x+13\right)
Combine 3x and -5x to get -2x.
6x^{3}+5x^{2}-2x-12-\left(4x^{3}-9x+13\right)
Combine -4x^{2} and 9x^{2} to get 5x^{2}.
6x^{3}+5x^{2}-2x-12-4x^{3}+9x-13
To find the opposite of 4x^{3}-9x+13, find the opposite of each term.
2x^{3}+5x^{2}-2x-12+9x-13
Combine 6x^{3} and -4x^{3} to get 2x^{3}.
2x^{3}+5x^{2}+7x-12-13
Combine -2x and 9x to get 7x.
2x^{3}+5x^{2}+7x-25
Subtract 13 from -12 to get -25.
6x^{3}-4x^{2}-2x-12+9x^{2}-\left(4x^{3}-9x+13\right)
Combine 3x and -5x to get -2x.
6x^{3}+5x^{2}-2x-12-\left(4x^{3}-9x+13\right)
Combine -4x^{2} and 9x^{2} to get 5x^{2}.
6x^{3}+5x^{2}-2x-12-4x^{3}+9x-13
To find the opposite of 4x^{3}-9x+13, find the opposite of each term.
2x^{3}+5x^{2}-2x-12+9x-13
Combine 6x^{3} and -4x^{3} to get 2x^{3}.
2x^{3}+5x^{2}+7x-12-13
Combine -2x and 9x to get 7x.
2x^{3}+5x^{2}+7x-25
Subtract 13 from -12 to get -25.