frac{24x(x^{3}+1)^{3/2}-3x^{2}(72x^{2}(x^3+1)^7/2)}{16(x^3+1)^3/2} eching

$$\frac { 24 x ( x ^ { 3 } + 1 ) ^ { 3 / 2 } - 3 x ^ { 2 } ( 72 x ^ { 2 } ( x ^ { 3 } + 1 ) ^ { 7 / 2 } ) } { 16 ( x ^ { 3 } + 1 ) ^ { 3 / 2 } }$$

Baholash

$$-\frac{27x^{10}}{2}-27x^{7}-\frac{27x^{4}}{2}+\frac{3x}{2}$$

Qisqa yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 2 ni qo‘shib, 4 ni oling.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-3x^{4}\times 72\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

216 hosil qilish uchun 3 va 72 ni ko'paytirish.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-216x^{4}\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}\left(-9x^{9}-18x^{6}-9x^{3}+1\right)}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Surat va maxrajdagi ikkala 8\left(x^{3}+1\right)^{\frac{3}{2}} ni qisqartiring.

$$\frac{3x\left(-9x^{9}-18x^{6}-9x^{3}+1\right)}{2}$$

Ifodani kengaytiring.

$$\frac{-27x^{10}-54x^{7}-27x^{4}+3x}{2}$$

Omil

$$\frac{3x\left(1-9x^{3}-18x^{6}-9x^{9}\right)}{2}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 2 ni qo‘shib, 4 ni oling.

$$factor(\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-3x^{4}\times 72\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

216 hosil qilish uchun 3 va 72 ni ko'paytirish.

$$factor(\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-216x^{4}\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-216x^{4}\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}} ichida hali faktorlanmagan ifodalarni faktorlang.

$$factor(\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}\left(-9x^{9}-18x^{6}-9x^{3}+1\right)}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

Surat va maxrajdagi ikkala 8\left(x^{3}+1\right)^{\frac{3}{2}} ni qisqartiring.

$$factor(\frac{3x\left(-9x^{9}-18x^{6}-9x^{3}+1\right)}{2})$$

3x ga -9x^{9}-18x^{6}-9x^{3}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$factor(\frac{-27x^{10}-54x^{7}-27x^{4}+3x}{2})$$

Hisoblang: -27x^{10}-54x^{7}-27x^{4}+3x. 3 omili.

$$3\left(-9x^{10}-18x^{7}-9x^{4}+x\right)$$

Hisoblang: -9x^{10}-18x^{7}-9x^{4}+x. x omili.

$$x\left(-9x^{9}-18x^{6}-9x^{3}+1\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing. Qisqartirish. Koʻphadli -9x^{9}-18x^{6}-9x^{3}+1 faktorlanmagan, chunki unda ratsional ildizlar topilmadi.

$$\frac{3x\left(-9x^{9}-18x^{6}-9x^{3}+1\right)}{2}$$