16q^9-16q eching

$$16 q ^ { 9 } - 16 q$$

Omil

$$16q\left(q-1\right)\left(q+1\right)\left(q^{2}+1\right)\left(q^{4}+1\right)$$

Yechim qadamlari

16 omili.

$$16\left(q^{9}-q\right)$$

Hisoblang: q^{9}-q. q omili.

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

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

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

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

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

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

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

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

$$16q\left(q-1\right)\left(q+1\right)\left(q^{2}+1\right)\left(q^{4}+1\right)$$

Baholash

$$16q\left(q^{8}-1\right)$$