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2x\left(x^{3}+3x^{2}+3x+1\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.
2x^{4}+6x^{3}+6x^{2}+2x
Use the distributive property to multiply 2x by x^{3}+3x^{2}+3x+1.
2x\left(x^{3}+3x^{2}+3x+1\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.
2x^{4}+6x^{3}+6x^{2}+2x
Use the distributive property to multiply 2x by x^{3}+3x^{2}+3x+1.