(5x^3+1)^3 eching

$$( 5 x ^ { 3 } + 1 ) ^ { 3 }$$

Kengaytirish

$$125x^{9}+75x^{6}+15x^{3}+1$$

Yechim qadamlari

\left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} binom teoremasini \left(5x^{3}+1\right)^{3} kengaytirilishi uchun ishlating.

$$125\left(x^{3}\right)^{3}+75\left(x^{3}\right)^{2}+15x^{3}+1$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 3 ni ko‘paytirib, 9 ni oling.

$$125x^{9}+75\left(x^{3}\right)^{2}+15x^{3}+1$$

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

$$125x^{9}+75x^{6}+15x^{3}+1$$

Baholash

$$\left(5x^{3}+1\right)^{3}$$

Yechim qadamlari

\left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} binom teoremasini \left(5x^{3}+1\right)^{3} kengaytirilishi uchun ishlating.

$$125\left(x^{3}\right)^{3}+75\left(x^{3}\right)^{2}+15x^{3}+1$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 3 ni ko‘paytirib, 9 ni oling.

$$125x^{9}+75\left(x^{3}\right)^{2}+15x^{3}+1$$

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

$$125x^{9}+75x^{6}+15x^{3}+1$$