[4(-1/2a^{2}b)^{3}]^{2}+5(-1/2a^{4}b^{2})^{3}+19(-1/2a^{3}b^2)^2(1/2a^6b^2) eching

$$[ 4 ( - \frac { 1 } { 2 } a ^ { 2 } b ) ^ { 3 } ] ^ { 2 } + 5 ( - \frac { 1 } { 2 } a ^ { 4 } b ^ { 2 } ) ^ { 3 } + 19 ( - \frac { 1 } { 2 } a ^ { 3 } b ^ { 2 } ) ^ { 2 } ( \frac { 1 } { 2 } a ^ { 6 } b ^ { 2 } )$$

Baholash

$$2b^{6}a^{12}$$

Yechim qadamlari

\left(-\frac{1}{2}a^{2}b\right)^{3} ni kengaytirish.

$$\left(4\left(-\frac{1}{2}\right)^{3}\left(a^{2}\right)^{3}b^{3}\right)^{2}+5\left(-\frac{1}{2}a^{4}b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 3 ni ko‘paytirib, 6 ni oling.

$$\left(4\left(-\frac{1}{2}\right)^{3}a^{6}b^{3}\right)^{2}+5\left(-\frac{1}{2}a^{4}b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

3 daraja ko‘rsatkichini -\frac{1}{2} ga hisoblang va -\frac{1}{8} ni qiymatni oling.

$$\left(4\left(-\frac{1}{8}\right)a^{6}b^{3}\right)^{2}+5\left(-\frac{1}{2}a^{4}b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

-\frac{1}{2} hosil qilish uchun 4 va -\frac{1}{8} ni ko'paytirish.

$$\left(-\frac{1}{2}a^{6}b^{3}\right)^{2}+5\left(-\frac{1}{2}a^{4}b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

\left(-\frac{1}{2}a^{6}b^{3}\right)^{2} ni kengaytirish.

$$\left(-\frac{1}{2}\right)^{2}\left(a^{6}\right)^{2}\left(b^{3}\right)^{2}+5\left(-\frac{1}{2}a^{4}b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 6 va 2 ni ko‘paytirib, 12 ni oling.

$$\left(-\frac{1}{2}\right)^{2}a^{12}\left(b^{3}\right)^{2}+5\left(-\frac{1}{2}a^{4}b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 2 ni ko‘paytirib, 6 ni oling.

$$\left(-\frac{1}{2}\right)^{2}a^{12}b^{6}+5\left(-\frac{1}{2}a^{4}b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

2 daraja ko‘rsatkichini -\frac{1}{2} ga hisoblang va \frac{1}{4} ni qiymatni oling.

$$\frac{1}{4}a^{12}b^{6}+5\left(-\frac{1}{2}a^{4}b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

\left(-\frac{1}{2}a^{4}b^{2}\right)^{3} ni kengaytirish.

$$\frac{1}{4}a^{12}b^{6}+5\left(-\frac{1}{2}\right)^{3}\left(a^{4}\right)^{3}\left(b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va 3 ni ko‘paytirib, 12 ni oling.

$$\frac{1}{4}a^{12}b^{6}+5\left(-\frac{1}{2}\right)^{3}a^{12}\left(b^{2}\right)^{3}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 3 ni ko‘paytirib, 6 ni oling.

$$\frac{1}{4}a^{12}b^{6}+5\left(-\frac{1}{2}\right)^{3}a^{12}b^{6}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

3 daraja ko‘rsatkichini -\frac{1}{2} ga hisoblang va -\frac{1}{8} ni qiymatni oling.

$$\frac{1}{4}a^{12}b^{6}+5\left(-\frac{1}{8}\right)a^{12}b^{6}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

-\frac{5}{8} hosil qilish uchun 5 va -\frac{1}{8} ni ko'paytirish.

$$\frac{1}{4}a^{12}b^{6}-\frac{5}{8}a^{12}b^{6}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

-\frac{3}{8}a^{12}b^{6} ni olish uchun \frac{1}{4}a^{12}b^{6} va -\frac{5}{8}a^{12}b^{6} ni birlashtirish.

$$-\frac{3}{8}a^{12}b^{6}+19\left(-\frac{1}{2}a^{3}b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

\left(-\frac{1}{2}a^{3}b^{2}\right)^{2} ni kengaytirish.

$$-\frac{3}{8}a^{12}b^{6}+19\left(-\frac{1}{2}\right)^{2}\left(a^{3}\right)^{2}\left(b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 2 ni ko‘paytirib, 6 ni oling.

$$-\frac{3}{8}a^{12}b^{6}+19\left(-\frac{1}{2}\right)^{2}a^{6}\left(b^{2}\right)^{2}\left(\frac{1}{2}a^{6}b^{2}\right)$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

$$-\frac{3}{8}a^{12}b^{6}+19\left(-\frac{1}{2}\right)^{2}a^{6}b^{4}\left(\frac{1}{2}a^{6}b^{2}\right)$$

2 daraja ko‘rsatkichini -\frac{1}{2} ga hisoblang va \frac{1}{4} ni qiymatni oling.

$$-\frac{3}{8}a^{12}b^{6}+19\times \frac{1}{4}a^{6}b^{4}\left(\frac{1}{2}a^{6}b^{2}\right)$$

\frac{19}{4} hosil qilish uchun 19 va \frac{1}{4} ni ko'paytirish.

$$-\frac{3}{8}a^{12}b^{6}+\frac{19}{4}a^{6}b^{4}\left(\frac{1}{2}a^{6}b^{2}\right)$$

\frac{1}{2}a^{6}b^{2} atrofidagi qavslarni olib tashlang.

$$-\frac{3}{8}a^{12}b^{6}+\frac{19}{4}a^{6}b^{4}\times \frac{1}{2}a^{6}b^{2}$$

\frac{19}{8} hosil qilish uchun \frac{19}{4} va \frac{1}{2} ni ko'paytirish.

$$-\frac{3}{8}a^{12}b^{6}+\frac{19}{8}a^{6}b^{4}a^{6}b^{2}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 6 va 6 ni qo‘shib, 12 ni oling.

$$-\frac{3}{8}a^{12}b^{6}+\frac{19}{8}a^{12}b^{4}b^{2}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 2 ni qo‘shib, 6 ni oling.

$$-\frac{3}{8}a^{12}b^{6}+\frac{19}{8}a^{12}b^{6}$$

2a^{12}b^{6} ni olish uchun -\frac{3}{8}a^{12}b^{6} va \frac{19}{8}a^{12}b^{6} ni birlashtirish.

$$2a^{12}b^{6}$$