a^4-b^4+a^4b^4-1 eching

$$a ^ { 4 } - b ^ { 4 } + a ^ { 4 } b ^ { 4 } - 1$$

Omil

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

Yechim qadamlari

a^{4}-b^{4}+a^{4}b^{4}-1=\left(a^{4}b^{4}+a^{4}\right)+\left(-b^{4}-1\right) misolini guruhlang hamda a^{4} ni birinchi va -1 ni ikkinchi guruhdan ajrating.

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

Distributiv funktsiyasidan foydalangan holda b^{4}+1 umumiy terminini chiqaring.

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

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

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

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

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

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

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

Baholash

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