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\frac{1}{27}\left(x^{3}+9x^{2}+27x+27\right)\left(x-1\right)^{2}\left(x-4\right)
Utilitzeu el teorema del binomi \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} per desenvolupar \left(x+3\right)^{3}.
\frac{1}{27}\left(x^{3}+9x^{2}+27x+27\right)\left(x^{2}-2x+1\right)\left(x-4\right)
Utilitzeu el teorema del binomi \left(a-b\right)^{2}=a^{2}-2ab+b^{2} per desenvolupar \left(x-1\right)^{2}.
\left(\frac{1}{27}x^{3}+\frac{1}{3}x^{2}+x+1\right)\left(x^{2}-2x+1\right)\left(x-4\right)
Utilitzeu la propietat distributiva per multiplicar \frac{1}{27} per x^{3}+9x^{2}+27x+27.
\left(\frac{1}{27}x^{5}+\frac{7}{27}x^{4}+\frac{10}{27}x^{3}-\frac{2}{3}x^{2}-x+1\right)\left(x-4\right)
Utilitzeu la propietat distributiva per multiplicar \frac{1}{27}x^{3}+\frac{1}{3}x^{2}+x+1 per x^{2}-2x+1 i combinar-los com termes.
\frac{1}{27}x^{6}+\frac{1}{9}x^{5}-\frac{2}{3}x^{4}-\frac{58}{27}x^{3}+\frac{5}{3}x^{2}+5x-4
Utilitzeu la propietat distributiva per multiplicar \frac{1}{27}x^{5}+\frac{7}{27}x^{4}+\frac{10}{27}x^{3}-\frac{2}{3}x^{2}-x+1 per x-4 i combinar-los com termes.
\frac{1}{27}\left(x^{3}+9x^{2}+27x+27\right)\left(x-1\right)^{2}\left(x-4\right)
Utilitzeu el teorema del binomi \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} per desenvolupar \left(x+3\right)^{3}.
\frac{1}{27}\left(x^{3}+9x^{2}+27x+27\right)\left(x^{2}-2x+1\right)\left(x-4\right)
Utilitzeu el teorema del binomi \left(a-b\right)^{2}=a^{2}-2ab+b^{2} per desenvolupar \left(x-1\right)^{2}.
\left(\frac{1}{27}x^{3}+\frac{1}{3}x^{2}+x+1\right)\left(x^{2}-2x+1\right)\left(x-4\right)
Utilitzeu la propietat distributiva per multiplicar \frac{1}{27} per x^{3}+9x^{2}+27x+27.
\left(\frac{1}{27}x^{5}+\frac{7}{27}x^{4}+\frac{10}{27}x^{3}-\frac{2}{3}x^{2}-x+1\right)\left(x-4\right)
Utilitzeu la propietat distributiva per multiplicar \frac{1}{27}x^{3}+\frac{1}{3}x^{2}+x+1 per x^{2}-2x+1 i combinar-los com termes.
\frac{1}{27}x^{6}+\frac{1}{9}x^{5}-\frac{2}{3}x^{4}-\frac{58}{27}x^{3}+\frac{5}{3}x^{2}+5x-4
Utilitzeu la propietat distributiva per multiplicar \frac{1}{27}x^{5}+\frac{7}{27}x^{4}+\frac{10}{27}x^{3}-\frac{2}{3}x^{2}-x+1 per x-4 i combinar-los com termes.