1(3a+2b)^2-(3a-2b)^2 eching

$$1 ( 3 a + 2 b ) ^ { 2 } - ( 3 a - 2 b ) ^ { 2 }$$

Baholash

$$24ab$$

Yechim qadamlari

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

$$1\left(9a^{2}+12ab+4b^{2}\right)-\left(3a-2b\right)^{2}$$

1 ga 9a^{2}+12ab+4b^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9a^{2}+12ab+4b^{2}-\left(3a-2b\right)^{2}$$

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

$$9a^{2}+12ab+4b^{2}-\left(9a^{2}-12ab+4b^{2}\right)$$

9a^{2}-12ab+4b^{2} teskarisini topish uchun har birining teskarisini toping.

$$9a^{2}+12ab+4b^{2}-9a^{2}+12ab-4b^{2}$$

0 ni olish uchun 9a^{2} va -9a^{2} ni birlashtirish.

$$12ab+4b^{2}+12ab-4b^{2}$$

24ab ni olish uchun 12ab va 12ab ni birlashtirish.

$$24ab+4b^{2}-4b^{2}$$

0 ni olish uchun 4b^{2} va -4b^{2} ni birlashtirish.

$$24ab$$

Kengaytirish

$$24ab$$

Yechim qadamlari

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

$$1\left(9a^{2}+12ab+4b^{2}\right)-\left(3a-2b\right)^{2}$$

1 ga 9a^{2}+12ab+4b^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9a^{2}+12ab+4b^{2}-\left(3a-2b\right)^{2}$$

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

$$9a^{2}+12ab+4b^{2}-\left(9a^{2}-12ab+4b^{2}\right)$$

9a^{2}-12ab+4b^{2} teskarisini topish uchun har birining teskarisini toping.

$$9a^{2}+12ab+4b^{2}-9a^{2}+12ab-4b^{2}$$

0 ni olish uchun 9a^{2} va -9a^{2} ni birlashtirish.

$$12ab+4b^{2}+12ab-4b^{2}$$

24ab ni olish uchun 12ab va 12ab ni birlashtirish.

$$24ab+4b^{2}-4b^{2}$$

0 ni olish uchun 4b^{2} va -4b^{2} ni birlashtirish.

$$24ab$$