Resolver 3u^3y^4-3u^3

$$3 u ^ { 3 } y ^ { 4 } - 3 u ^ { 3 }$$

Faktorizatu

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

Ebazpidea

Deskonposatu 3.

$$3\left(u^{3}y^{4}-u^{3}\right)$$

Kasurako: u^{3}y^{4}-u^{3}. Deskonposatu u^{3}.

$$u^{3}\left(y^{4}-1\right)$$

Kasurako: y^{4}-1. Berridatzi y^{4}-1 honela: \left(y^{2}\right)^{2}-1^{2}. Kuboen diferentzia faktorizatzeko, erabili a^{2}-b^{2}=\left(a-b\right)\left(a+b\right) araua.

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

Kasurako: y^{2}-1. Berridatzi y^{2}-1 honela: y^{2}-1^{2}. Kuboen diferentzia faktorizatzeko, erabili a^{2}-b^{2}=\left(a-b\right)\left(a+b\right) araua.

$$\left(y-1\right)\left(y+1\right)$$

Berridatzi faktorizatutako adierazpen osoa. y^{2}+1 polinomioa ez dago faktorizatuta, ez baitu erro arrazionalik.

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

Ebaluatu

$$3u^{3}\left(y^{4}-1\right)$$