1-m^16 eching

$$1 - m ^ { 16 }$$

Omil

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

Yechim qadamlari

1-m^{16} ni 1^{2}-\left(-m^{8}\right)^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Shartlarni qayta saralash.

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

Hisoblang: -m^{8}+1. -m^{8}+1 ni 1^{2}-\left(-m^{4}\right)^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Shartlarni qayta saralash.

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

Hisoblang: -m^{4}+1. -m^{4}+1 ni 1^{2}-\left(-m^{2}\right)^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Shartlarni qayta saralash.

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

Hisoblang: -m^{2}+1. -m^{2}+1 ni 1^{2}-m^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Shartlarni qayta saralash.

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

Toʻliq ajratilgan ifodani qaytadan yozing. Quyidagi koʻphadlar faktorlanmagan, ularda hech qanday ratsional ildizlar topilmadi: m^{2}+1,m^{4}+1,m^{8}+1.

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

Baholash

$$1-m^{16}$$