x^12-a^12= eching

$$x ^ { 12 } - a ^ { 12 } =$$

Omil

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

Yechim qadamlari

x^{12}-a^{12} ni \left(x^{6}\right)^{2}-\left(a^{6}\right)^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(x^{6}-a^{6}\right)\left(x^{6}+a^{6}\right)$$

Hisoblang: x^{6}-a^{6}. x^{6}-a^{6} ni \left(x^{3}\right)^{2}-\left(a^{3}\right)^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(x^{3}-a^{3}\right)\left(x^{3}+a^{3}\right)$$

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

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

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

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

Hisoblang: x^{6}+a^{6}. x^{6}+a^{6} ni \left(x^{2}\right)^{3}+\left(a^{2}\right)^{3} sifatida qaytadan yozish. Kublar yigʻindisini ushbu formula bilan hisoblash mumkin: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).

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

Toʻliq ajratilgan ifodani qaytadan yozing.

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

Baholash

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