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3x^{3}-12x^{2}+18x-9+5\left(-t^{3}+2x^{2}-9x+17\right)
Use the distributive property to multiply 3 by x^{3}-4x^{2}+6x-3.
3x^{3}-12x^{2}+18x-9+5\left(-t^{3}\right)+10x^{2}-45x+85
Use the distributive property to multiply 5 by -t^{3}+2x^{2}-9x+17.
3x^{3}-2x^{2}+18x-9+5\left(-t^{3}\right)-45x+85
Combine -12x^{2} and 10x^{2} to get -2x^{2}.
3x^{3}-2x^{2}-27x-9+5\left(-t^{3}\right)+85
Combine 18x and -45x to get -27x.
3x^{3}-2x^{2}-27x+76+5\left(-t^{3}\right)
Add -9 and 85 to get 76.
3x^{3}-2x^{2}-27x+76-5t^{3}
Multiply 5 and -1 to get -5.
3x^{3}-12x^{2}+18x-9+5\left(-t^{3}+2x^{2}-9x+17\right)
Use the distributive property to multiply 3 by x^{3}-4x^{2}+6x-3.
3x^{3}-12x^{2}+18x-9+5\left(-t^{3}\right)+10x^{2}-45x+85
Use the distributive property to multiply 5 by -t^{3}+2x^{2}-9x+17.
3x^{3}-2x^{2}+18x-9+5\left(-t^{3}\right)-45x+85
Combine -12x^{2} and 10x^{2} to get -2x^{2}.
3x^{3}-2x^{2}-27x-9+5\left(-t^{3}\right)+85
Combine 18x and -45x to get -27x.
3x^{3}-2x^{2}-27x+76+5\left(-t^{3}\right)
Add -9 and 85 to get 76.
3x^{3}-2x^{2}-27x+76-5t^{3}
Multiply 5 and -1 to get -5.