49x^4-4(x^2-3x)^2 eching

$$49 x ^ { 4 } - 4 ( x ^ { 2 } - 3 x ) ^ { 2 }$$

Baholash

$$3\left(3x-2\right)\left(5x+6\right)x^{2}$$

Yechim qadamlari

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

$$49x^{4}-4\left(\left(x^{2}\right)^{2}-6x^{2}x+9x^{2}\right)$$

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

$$49x^{4}-4\left(x^{4}-6x^{2}x+9x^{2}\right)$$

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

$$49x^{4}-4\left(x^{4}-6x^{3}+9x^{2}\right)$$

-4 ga x^{4}-6x^{3}+9x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$49x^{4}-4x^{4}+24x^{3}-36x^{2}$$

45x^{4} ni olish uchun 49x^{4} va -4x^{4} ni birlashtirish.

$$45x^{4}+24x^{3}-36x^{2}$$

Kengaytirish

$$45x^{4}+24x^{3}-36x^{2}$$

Yechim qadamlari

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

$$49x^{4}-4\left(\left(x^{2}\right)^{2}-6x^{2}x+9x^{2}\right)$$

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

$$49x^{4}-4\left(x^{4}-6x^{2}x+9x^{2}\right)$$

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

$$49x^{4}-4\left(x^{4}-6x^{3}+9x^{2}\right)$$

-4 ga x^{4}-6x^{3}+9x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$49x^{4}-4x^{4}+24x^{3}-36x^{2}$$

45x^{4} ni olish uchun 49x^{4} va -4x^{4} ni birlashtirish.

$$45x^{4}+24x^{3}-36x^{2}$$