9(2a+3b)^2-4(3a-2b)^2 eching

$$9 ( 2 a + 3 b ) ^ { 2 } - 4 ( 3 a - 2 b ) ^ { 2 }$$

Baholash

$$13b\left(12a+5b\right)$$

Yechim qadamlari

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

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

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

$$36a^{2}+108ab+81b^{2}-4\left(3a-2b\right)^{2}$$

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

$$36a^{2}+108ab+81b^{2}-4\left(9a^{2}-12ab+4b^{2}\right)$$

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

$$36a^{2}+108ab+81b^{2}-36a^{2}+48ab-16b^{2}$$

0 ni olish uchun 36a^{2} va -36a^{2} ni birlashtirish.

$$108ab+81b^{2}+48ab-16b^{2}$$

156ab ni olish uchun 108ab va 48ab ni birlashtirish.

$$156ab+81b^{2}-16b^{2}$$

65b^{2} ni olish uchun 81b^{2} va -16b^{2} ni birlashtirish.

$$156ab+65b^{2}$$

Kengaytirish

$$156ab+65b^{2}$$

Yechim qadamlari

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

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

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

$$36a^{2}+108ab+81b^{2}-4\left(3a-2b\right)^{2}$$

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

$$36a^{2}+108ab+81b^{2}-4\left(9a^{2}-12ab+4b^{2}\right)$$

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

$$36a^{2}+108ab+81b^{2}-36a^{2}+48ab-16b^{2}$$

0 ni olish uchun 36a^{2} va -36a^{2} ni birlashtirish.

$$108ab+81b^{2}+48ab-16b^{2}$$

156ab ni olish uchun 108ab va 48ab ni birlashtirish.

$$156ab+81b^{2}-16b^{2}$$

65b^{2} ni olish uchun 81b^{2} va -16b^{2} ni birlashtirish.

$$156ab+65b^{2}$$