(a-3b)^2-2a(b-a)+b(3a+b) eching

$$( a - 3 b ) ^ { 2 } - 2 a ( b - a ) + b ( 3 a + b )$$

Baholash

$$3a^{2}-5ab+10b^{2}$$

Yechim qadamlari

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

$$a^{2}-6ab+9b^{2}-2a\left(b-a\right)+b\left(3a+b\right)$$

b ga 3a+b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$a^{2}-6ab+9b^{2}-2a\left(b-a\right)+3ba+b^{2}$$

-2a ga b-a ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$a^{2}-6ab+9b^{2}-2ab+2a^{2}+3ba+b^{2}$$

-8ab ni olish uchun -6ab va -2ab ni birlashtirish.

$$a^{2}-8ab+9b^{2}+2a^{2}+3ba+b^{2}$$

3a^{2} ni olish uchun a^{2} va 2a^{2} ni birlashtirish.

$$3a^{2}-8ab+9b^{2}+3ba+b^{2}$$

-5ab ni olish uchun -8ab va 3ba ni birlashtirish.

$$3a^{2}-5ab+9b^{2}+b^{2}$$

10b^{2} ni olish uchun 9b^{2} va b^{2} ni birlashtirish.

$$3a^{2}-5ab+10b^{2}$$

Kengaytirish

$$3a^{2}-5ab+10b^{2}$$

Yechim qadamlari

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

$$a^{2}-6ab+9b^{2}-2a\left(b-a\right)+b\left(3a+b\right)$$

b ga 3a+b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$a^{2}-6ab+9b^{2}-2a\left(b-a\right)+3ba+b^{2}$$

-2a ga b-a ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$a^{2}-6ab+9b^{2}-2ab+2a^{2}+3ba+b^{2}$$

-8ab ni olish uchun -6ab va -2ab ni birlashtirish.

$$a^{2}-8ab+9b^{2}+2a^{2}+3ba+b^{2}$$

3a^{2} ni olish uchun a^{2} va 2a^{2} ni birlashtirish.

$$3a^{2}-8ab+9b^{2}+3ba+b^{2}$$

-5ab ni olish uchun -8ab va 3ba ni birlashtirish.

$$3a^{2}-5ab+9b^{2}+b^{2}$$

10b^{2} ni olish uchun 9b^{2} va b^{2} ni birlashtirish.

$$3a^{2}-5ab+10b^{2}$$