Resol f(y)=(y+3)^3(5y+1)^2(3y^2-4)

$$f ( y ) = ( y + 3 ) ^ { 3 } ( 5 y + 1 ) ^ { 2 } ( 3 y ^ { 2 } - 4 )$$

Calcula

$$\left(3y^{2}-4\right)\left(5y+1\right)^{2}\left(y+3\right)^{3}$$

Passos de solució

Utilitzeu el teorema del binomi \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} per desenvolupar \left(y+3\right)^{3}.

$$\left(y^{3}+9y^{2}+27y+27\right)\left(5y+1\right)^{2}\left(3y^{2}-4\right)$$

Utilitzeu el teorema del binomi \left(a+b\right)^{2}=a^{2}+2ab+b^{2} per desenvolupar \left(5y+1\right)^{2}.

$$\left(y^{3}+9y^{2}+27y+27\right)\left(25y^{2}+10y+1\right)\left(3y^{2}-4\right)$$

Utilitzeu la propietat distributiva per multiplicar y^{3}+9y^{2}+27y+27 per 25y^{2}+10y+1 i combinar-los com termes.

$$\left(25y^{5}+235y^{4}+766y^{3}+954y^{2}+297y+27\right)\left(3y^{2}-4\right)$$

Utilitzeu la propietat distributiva per multiplicar 25y^{5}+235y^{4}+766y^{3}+954y^{2}+297y+27 per 3y^{2}-4 i combinar-los com termes.

$$75y^{7}+2198y^{5}+705y^{6}+1922y^{4}-2173y^{3}-3735y^{2}-1188y-108$$

Expandiu

$$75y^{7}+705y^{6}+2198y^{5}+1922y^{4}-2173y^{3}-3735y^{2}-1188y-108$$

Passos de solució

Utilitzeu el teorema del binomi \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} per desenvolupar \left(y+3\right)^{3}.

$$\left(y^{3}+9y^{2}+27y+27\right)\left(5y+1\right)^{2}\left(3y^{2}-4\right)$$

Utilitzeu el teorema del binomi \left(a+b\right)^{2}=a^{2}+2ab+b^{2} per desenvolupar \left(5y+1\right)^{2}.

$$\left(y^{3}+9y^{2}+27y+27\right)\left(25y^{2}+10y+1\right)\left(3y^{2}-4\right)$$

Utilitzeu la propietat distributiva per multiplicar y^{3}+9y^{2}+27y+27 per 25y^{2}+10y+1 i combinar-los com termes.

$$\left(25y^{5}+235y^{4}+766y^{3}+954y^{2}+297y+27\right)\left(3y^{2}-4\right)$$

Utilitzeu la propietat distributiva per multiplicar 25y^{5}+235y^{4}+766y^{3}+954y^{2}+297y+27 per 3y^{2}-4 i combinar-los com termes.

$$75y^{7}+2198y^{5}+705y^{6}+1922y^{4}-2173y^{3}-3735y^{2}-1188y-108$$