x^3y^3-x^3-y^3+1= eching

$$x ^ { 3 } y ^ { 3 } - x ^ { 3 } - y ^ { 3 } + 1 =$$

Omil

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

Yechim qadamlari

x^{3}y^{3}-x^{3}-y^{3}+1=\left(x^{3}y^{3}-x^{3}\right)+\left(-y^{3}+1\right) misolini guruhlang hamda x^{3} ni birinchi va -1 ni ikkinchi guruhdan ajrating.

$$x^{3}\left(y^{3}-1\right)-\left(y^{3}-1\right)$$

Distributiv funktsiyasidan foydalangan holda y^{3}-1 umumiy terminini chiqaring.

$$\left(y^{3}-1\right)\left(x^{3}-1\right)$$

Hisoblang: y^{3}-1. y^{3}-1 ni y^{3}-1^{3} sifatida qaytadan yozish. Kublarning farqini ushbu formula bilan hisoblash mumkin: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

Hisoblang: x^{3}-1. x^{3}-1 ni x^{3}-1^{3} sifatida qaytadan yozish. Kublarning farqini ushbu formula bilan hisoblash mumkin: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

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

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

Baholash

$$1+\left(xy\right)^{3}-y^{3}-x^{3}$$