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3x^{3}+12x^{2}+2x\left(x-7\right)
Use the distributive property to multiply 3 by x^{3}+4x^{2}.
3x^{3}+12x^{2}+2x^{2}-14x
Use the distributive property to multiply 2x by x-7.
3x^{3}+14x^{2}-14x
Combine 12x^{2} and 2x^{2} to get 14x^{2}.
3x^{3}+12x^{2}+2x\left(x-7\right)
Use the distributive property to multiply 3 by x^{3}+4x^{2}.
3x^{3}+12x^{2}+2x^{2}-14x
Use the distributive property to multiply 2x by x-7.
3x^{3}+14x^{2}-14x
Combine 12x^{2} and 2x^{2} to get 14x^{2}.