Resolver 1-m^16

$$1 - m ^ { 16 }$$

Faktorizatu

$$\left(m-1\right)\left(m+1\right)\left(m^{2}+1\right)\left(m^{4}+1\right)\left(-m^{8}-1\right)$$

Ebazpidea

Berridatzi 1-m^{16} honela: 1^{2}-\left(-m^{8}\right)^{2}. Kuboen diferentzia faktorizatzeko, erabili a^{2}-b^{2}=\left(a-b\right)\left(a+b\right) araua.

$$\left(1+m^{8}\right)\left(1-m^{8}\right)$$

Berrantolatu gaiak.

$$\left(m^{8}+1\right)\left(-m^{8}+1\right)$$

Kasurako: -m^{8}+1. Berridatzi -m^{8}+1 honela: 1^{2}-\left(-m^{4}\right)^{2}. Kuboen diferentzia faktorizatzeko, erabili a^{2}-b^{2}=\left(a-b\right)\left(a+b\right) araua.

$$\left(1+m^{4}\right)\left(1-m^{4}\right)$$

Berrantolatu gaiak.

$$\left(m^{4}+1\right)\left(-m^{4}+1\right)$$

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

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

Berrantolatu gaiak.

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

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

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

Berrantolatu gaiak.

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

Berridatzi faktorizatutako adierazpen osoa. Polinomio hauek ez daude faktorizatuta, ez baitute erro arrazionalik: m^{2}+1,m^{4}+1,m^{8}+1.

$$\left(-m+1\right)\left(m+1\right)\left(m^{2}+1\right)\left(m^{4}+1\right)\left(m^{8}+1\right)$$

Ebaluatu

$$1-m^{16}$$