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

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

Baholash

$$-7b^{4}$$

Yechim qadamlari

3a-2b ga 3a+2b ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

Hisoblang: \left(9a^{2}-4b^{2}\right)\left(9a^{2}+4b^{2}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(9a^{2}\right)^{2} ni kengaytirish.

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

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

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

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

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

\left(4b^{2}\right)^{2} ni kengaytirish.

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

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

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

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$81a^{4}-16b^{4}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

\left(-3a\right)^{4} ni kengaytirish.

$$81a^{4}-16b^{4}-\left(-3\right)^{4}a^{4}+\left(-3b^{2}\right)^{2}$$

4 daraja ko‘rsatkichini -3 ga hisoblang va 81 ni qiymatni oling.

$$81a^{4}-16b^{4}-81a^{4}+\left(-3b^{2}\right)^{2}$$

0 ni olish uchun 81a^{4} va -81a^{4} ni birlashtirish.

$$-16b^{4}+\left(-3b^{2}\right)^{2}$$

\left(-3b^{2}\right)^{2} ni kengaytirish.

$$-16b^{4}+\left(-3\right)^{2}\left(b^{2}\right)^{2}$$

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

$$-16b^{4}+\left(-3\right)^{2}b^{4}$$

2 daraja ko‘rsatkichini -3 ga hisoblang va 9 ni qiymatni oling.

$$-16b^{4}+9b^{4}$$

-7b^{4} ni olish uchun -16b^{4} va 9b^{4} ni birlashtirish.

$$-7b^{4}$$

Kengaytirish

$$-7b^{4}$$

Yechim qadamlari

3a-2b ga 3a+2b ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

Hisoblang: \left(9a^{2}-4b^{2}\right)\left(9a^{2}+4b^{2}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(9a^{2}\right)^{2} ni kengaytirish.

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

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

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

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

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

\left(4b^{2}\right)^{2} ni kengaytirish.

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

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

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

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$81a^{4}-16b^{4}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

\left(-3a\right)^{4} ni kengaytirish.

$$81a^{4}-16b^{4}-\left(-3\right)^{4}a^{4}+\left(-3b^{2}\right)^{2}$$

4 daraja ko‘rsatkichini -3 ga hisoblang va 81 ni qiymatni oling.

$$81a^{4}-16b^{4}-81a^{4}+\left(-3b^{2}\right)^{2}$$

0 ni olish uchun 81a^{4} va -81a^{4} ni birlashtirish.

$$-16b^{4}+\left(-3b^{2}\right)^{2}$$

\left(-3b^{2}\right)^{2} ni kengaytirish.

$$-16b^{4}+\left(-3\right)^{2}\left(b^{2}\right)^{2}$$

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

$$-16b^{4}+\left(-3\right)^{2}b^{4}$$

2 daraja ko‘rsatkichini -3 ga hisoblang va 9 ni qiymatni oling.

$$-16b^{4}+9b^{4}$$

-7b^{4} ni olish uchun -16b^{4} va 9b^{4} ni birlashtirish.

$$-7b^{4}$$