4left(2p+3qright)^2-left(3p-qright)^2 eching

$$4 { \left(2p+3q \right) }^{ 2 } - { \left(3p-q \right) }^{ 2 }$$

Baholash

$$\left(p+7q\right)\left(7p+5q\right)$$

Yechim qadamlari

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

$$4\left(4p^{2}+12pq+9q^{2}\right)-\left(3p-q\right)^{2}$$

4 ga 4p^{2}+12pq+9q^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16p^{2}+48pq+36q^{2}-\left(3p-q\right)^{2}$$

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

$$16p^{2}+48pq+36q^{2}-\left(9p^{2}-6pq+q^{2}\right)$$

9p^{2}-6pq+q^{2} teskarisini topish uchun har birining teskarisini toping.

$$16p^{2}+48pq+36q^{2}-9p^{2}+6pq-q^{2}$$

7p^{2} ni olish uchun 16p^{2} va -9p^{2} ni birlashtirish.

$$7p^{2}+48pq+36q^{2}+6pq-q^{2}$$

54pq ni olish uchun 48pq va 6pq ni birlashtirish.

$$7p^{2}+54pq+36q^{2}-q^{2}$$

35q^{2} ni olish uchun 36q^{2} va -q^{2} ni birlashtirish.

$$7p^{2}+54pq+35q^{2}$$

Kengaytirish

$$7p^{2}+54pq+35q^{2}$$

Yechim qadamlari

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

$$4\left(4p^{2}+12pq+9q^{2}\right)-\left(3p-q\right)^{2}$$

4 ga 4p^{2}+12pq+9q^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16p^{2}+48pq+36q^{2}-\left(3p-q\right)^{2}$$

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

$$16p^{2}+48pq+36q^{2}-\left(9p^{2}-6pq+q^{2}\right)$$

9p^{2}-6pq+q^{2} teskarisini topish uchun har birining teskarisini toping.

$$16p^{2}+48pq+36q^{2}-9p^{2}+6pq-q^{2}$$

7p^{2} ni olish uchun 16p^{2} va -9p^{2} ni birlashtirish.

$$7p^{2}+48pq+36q^{2}+6pq-q^{2}$$

54pq ni olish uchun 48pq va 6pq ni birlashtirish.

$$7p^{2}+54pq+36q^{2}-q^{2}$$

35q^{2} ni olish uchun 36q^{2} va -q^{2} ni birlashtirish.

$$7p^{2}+54pq+35q^{2}$$