a^{2}x^{3}-x^{3}b^{2}-a^2y^3+y^3b^2= eching

$$a ^ { 2 } x ^ { 3 } - x ^ { 3 } b ^ { 2 } - a ^ { 2 } y ^ { 3 } + y ^ { 3 } b ^ { 2 } =$$

Omil

$$\left(a-b\right)\left(x-y\right)\left(a+b\right)\left(x^{2}+xy+y^{2}\right)$$

Yechim qadamlari

a^{2}x^{3}-x^{3}b^{2}-a^{2}y^{3}+y^{3}b^{2}=\left(a^{2}x^{3}-x^{3}b^{2}\right)+\left(-a^{2}y^{3}+y^{3}b^{2}\right) misolini guruhlang hamda x^{3} ni birinchi va -y^{3} ni ikkinchi guruhdan ajrating.

$$x^{3}\left(a^{2}-b^{2}\right)-y^{3}\left(a^{2}-b^{2}\right)$$

Distributiv funktsiyasidan foydalangan holda a^{2}-b^{2} umumiy terminini chiqaring.

$$\left(a^{2}-b^{2}\right)\left(x^{3}-y^{3}\right)$$

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

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

Hisoblang: x^{3}-y^{3}. Kublarning farqini ushbu formula bilan hisoblash mumkin: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).

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

Toʻliq ajratilgan ifodani qaytadan yozing.

$$\left(a-b\right)\left(a+b\right)\left(x-y\right)\left(x^{2}+xy+y^{2}\right)$$

Baholash

$$\left(a^{2}-b^{2}\right)\left(x^{3}-y^{3}\right)$$