4a^2b*(-ab^2)*5ab-8a^4b^4= eching

$$4 a ^ { 2 } b \cdot ( - a b ^ { 2 } ) \cdot 5 a b - 8 a ^ { 4 } b ^ { 4 } =$$

Baholash

$$-28\left(ab\right)^{4}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$4a^{3}b\left(-a\right)b^{2}\times 5b-8a^{4}b^{4}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$4a^{3}b^{3}\left(-a\right)\times 5b-8a^{4}b^{4}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 1 ni qo‘shib, 4 ni oling.

$$4a^{3}b^{4}\left(-a\right)\times 5-8a^{4}b^{4}$$

20 hosil qilish uchun 4 va 5 ni ko'paytirish.

$$20a^{3}b^{4}\left(-a\right)-8a^{4}b^{4}$$

-20 hosil qilish uchun 20 va -1 ni ko'paytirish.

$$-20a^{3}b^{4}a-8a^{4}b^{4}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 1 ni qo‘shib, 4 ni oling.

$$-20a^{4}b^{4}-8a^{4}b^{4}$$

-28a^{4}b^{4} ni olish uchun -20a^{4}b^{4} va -8a^{4}b^{4} ni birlashtirish.

$$-28a^{4}b^{4}$$

a ga nisbatan hosilani topish

$$-112a^{3}b^{4}$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

$$2\left(-20a^{2}b^{4}\right)a^{2-1}+4\left(-8b^{4}\right)a^{4-1}$$

2 ni 4\times 5b\left(-1\right)ab^{2}ab marotabaga ko'paytirish.

$$\left(-40a^{2}b^{4}\right)a^{2-1}+4\left(-8b^{4}\right)a^{4-1}$$

2 dan 1 ni ayirish.

$$\left(-40a^{2}b^{4}\right)a^{1}+4\left(-8b^{4}\right)a^{4-1}$$

4 ni -8b^{4} marotabaga ko'paytirish.

$$\left(-40a^{2}b^{4}\right)a^{1}+\left(-32b^{4}\right)a^{4-1}$$

4 dan 1 ni ayirish.

$$\left(-40a^{2}b^{4}\right)a^{1}+\left(-32b^{4}\right)a^{3}$$

Har qanday t sharti uchun t^{1}=t.

$$\left(-40a^{2}b^{4}\right)a+\left(-32b^{4}\right)a^{3}$$