(x^2+2)^2*[5*(x^2+2)^2-3]*(2x) eching

$$( x ^ { 2 } + 2 ) ^ { 2 } \cdot [ 5 \cdot ( x ^ { 2 } + 2 ) ^ { 2 } - 3 ] \cdot ( 2 x )$$

Baholash

$$10x\left(x^{2}+2\right)^{4}-6x\left(x^{2}+2\right)^{2}$$

Yechim qadamlari

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

$$\left(\left(x^{2}\right)^{2}+4x^{2}+4\right)\left(5\left(x^{2}+2\right)^{2}-3\right)\times 2x$$

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

$$\left(x^{4}+4x^{2}+4\right)\left(5\left(x^{2}+2\right)^{2}-3\right)\times 2x$$

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

$$\left(x^{4}+4x^{2}+4\right)\left(5\left(\left(x^{2}\right)^{2}+4x^{2}+4\right)-3\right)\times 2x$$

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

$$\left(x^{4}+4x^{2}+4\right)\left(5\left(x^{4}+4x^{2}+4\right)-3\right)\times 2x$$

5 ga x^{4}+4x^{2}+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(x^{4}+4x^{2}+4\right)\left(5x^{4}+20x^{2}+20-3\right)\times 2x$$

17 olish uchun 20 dan 3 ni ayirish.

$$\left(x^{4}+4x^{2}+4\right)\left(5x^{4}+20x^{2}+17\right)\times 2x$$

x^{4}+4x^{2}+4 ga 5x^{4}+20x^{2}+17 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(5x^{8}+40x^{6}+117x^{4}+148x^{2}+68\right)\times 2x$$

5x^{8}+40x^{6}+117x^{4}+148x^{2}+68 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(10x^{8}+80x^{6}+234x^{4}+296x^{2}+136\right)x$$

10x^{8}+80x^{6}+234x^{4}+296x^{2}+136 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$10x^{9}+80x^{7}+234x^{5}+296x^{3}+136x$$

Kengaytirish

$$10x^{9}+80x^{7}+234x^{5}+296x^{3}+136x$$

Yechim qadamlari

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

$$\left(\left(x^{2}\right)^{2}+4x^{2}+4\right)\left(5\left(x^{2}+2\right)^{2}-3\right)\times 2x$$

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

$$\left(x^{4}+4x^{2}+4\right)\left(5\left(x^{2}+2\right)^{2}-3\right)\times 2x$$

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

$$\left(x^{4}+4x^{2}+4\right)\left(5\left(\left(x^{2}\right)^{2}+4x^{2}+4\right)-3\right)\times 2x$$

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

$$\left(x^{4}+4x^{2}+4\right)\left(5\left(x^{4}+4x^{2}+4\right)-3\right)\times 2x$$

5 ga x^{4}+4x^{2}+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(x^{4}+4x^{2}+4\right)\left(5x^{4}+20x^{2}+20-3\right)\times 2x$$

17 olish uchun 20 dan 3 ni ayirish.

$$\left(x^{4}+4x^{2}+4\right)\left(5x^{4}+20x^{2}+17\right)\times 2x$$

x^{4}+4x^{2}+4 ga 5x^{4}+20x^{2}+17 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(5x^{8}+40x^{6}+117x^{4}+148x^{2}+68\right)\times 2x$$

5x^{8}+40x^{6}+117x^{4}+148x^{2}+68 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(10x^{8}+80x^{6}+234x^{4}+296x^{2}+136\right)x$$

10x^{8}+80x^{6}+234x^{4}+296x^{2}+136 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$10x^{9}+80x^{7}+234x^{5}+296x^{3}+136x$$