1-a^8 eching

$$1 - a ^ { 8 }$$

Omil

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

Yechim qadamlari

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

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

Shartlarni qayta saralash.

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

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

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

Shartlarni qayta saralash.

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

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

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

Shartlarni qayta saralash.

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

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

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

Baholash

$$1-a^{8}$$