(2x^2-3x)^3 eching

$$( 2 x ^ { 2 } - 3 x ) ^ { 3 }$$

Baholash

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

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(2x^{2}-3x\right)^{3} kengaytirilishi uchun ishlating.

$$8\left(x^{2}\right)^{3}-36\left(x^{2}\right)^{2}x+54x^{2}x^{2}-27x^{3}$$

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

$$8x^{6}-36\left(x^{2}\right)^{2}x+54x^{2}x^{2}-27x^{3}$$

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

$$8x^{6}-36x^{4}x+54x^{2}x^{2}-27x^{3}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 1 ni qo‘shib, 5 ni oling.

$$8x^{6}-36x^{5}+54x^{2}x^{2}-27x^{3}$$

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

$$8x^{6}-36x^{5}+54x^{4}-27x^{3}$$

Kengaytirish

$$8x^{6}-36x^{5}+54x^{4}-27x^{3}$$

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(2x^{2}-3x\right)^{3} kengaytirilishi uchun ishlating.

$$8\left(x^{2}\right)^{3}-36\left(x^{2}\right)^{2}x+54x^{2}x^{2}-27x^{3}$$

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

$$8x^{6}-36\left(x^{2}\right)^{2}x+54x^{2}x^{2}-27x^{3}$$

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

$$8x^{6}-36x^{4}x+54x^{2}x^{2}-27x^{3}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 1 ni qo‘shib, 5 ni oling.

$$8x^{6}-36x^{5}+54x^{2}x^{2}-27x^{3}$$

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

$$8x^{6}-36x^{5}+54x^{4}-27x^{3}$$