y=(x-3)^2(x^2+4)^3 eching

$$y = ( x - 3 ) ^ { 2 } ( x ^ { 2 } + 4 ) ^ { 3 }$$

y uchun yechish

$$y=\left(x-3\right)^{2}\left(x^{2}+4\right)^{3}$$

Yechim qadamlari

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

$$y=\left(x^{2}-6x+9\right)\left(x^{2}+4\right)^{3}$$

\left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} binom teoremasini \left(x^{2}+4\right)^{3} kengaytirilishi uchun ishlating.

$$y=\left(x^{2}-6x+9\right)\left(\left(x^{2}\right)^{3}+12\left(x^{2}\right)^{2}+48x^{2}+64\right)$$

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

$$y=\left(x^{2}-6x+9\right)\left(x^{6}+12\left(x^{2}\right)^{2}+48x^{2}+64\right)$$

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

$$y=\left(x^{2}-6x+9\right)\left(x^{6}+12x^{4}+48x^{2}+64\right)$$

x^{2}-6x+9 ga x^{6}+12x^{4}+48x^{2}+64 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$y=x^{8}+21x^{6}+156x^{4}+496x^{2}-6x^{7}-72x^{5}-288x^{3}-384x+576$$