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

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

Baholash

$$\left(5a^{2}+27\right)\left(a^{2}+9\right)$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(a^{2}+9\right)^{2} kengaytirilishi uchun ishlating.

$$4\left(\left(a^{2}\right)^{2}+18a^{2}+81\right)-\left(a+3\right)\left(3-a\right)\left(a^{2}+9\right)$$

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

$$4\left(a^{4}+18a^{2}+81\right)-\left(a+3\right)\left(3-a\right)\left(a^{2}+9\right)$$

4 ga a^{4}+18a^{2}+81 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4a^{4}+72a^{2}+324-\left(a+3\right)\left(3-a\right)\left(a^{2}+9\right)$$

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

$$4a^{4}+72a^{2}+324-\left(-a^{2}+9\right)\left(a^{2}+9\right)$$

-a^{2}+9 ga a^{2}+9 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4a^{4}+72a^{2}+324-\left(-a^{4}+81\right)$$

-a^{4}+81 teskarisini topish uchun har birining teskarisini toping.

$$4a^{4}+72a^{2}+324+a^{4}-81$$

5a^{4} ni olish uchun 4a^{4} va a^{4} ni birlashtirish.

$$5a^{4}+72a^{2}+324-81$$

243 olish uchun 324 dan 81 ni ayirish.

$$5a^{4}+72a^{2}+243$$

Kengaytirish

$$5a^{4}+72a^{2}+243$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(a^{2}+9\right)^{2} kengaytirilishi uchun ishlating.

$$4\left(\left(a^{2}\right)^{2}+18a^{2}+81\right)-\left(a+3\right)\left(3-a\right)\left(a^{2}+9\right)$$

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

$$4\left(a^{4}+18a^{2}+81\right)-\left(a+3\right)\left(3-a\right)\left(a^{2}+9\right)$$

4 ga a^{4}+18a^{2}+81 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4a^{4}+72a^{2}+324-\left(a+3\right)\left(3-a\right)\left(a^{2}+9\right)$$

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

$$4a^{4}+72a^{2}+324-\left(-a^{2}+9\right)\left(a^{2}+9\right)$$

-a^{2}+9 ga a^{2}+9 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4a^{4}+72a^{2}+324-\left(-a^{4}+81\right)$$

-a^{4}+81 teskarisini topish uchun har birining teskarisini toping.

$$4a^{4}+72a^{2}+324+a^{4}-81$$

5a^{4} ni olish uchun 4a^{4} va a^{4} ni birlashtirish.

$$5a^{4}+72a^{2}+324-81$$

243 olish uchun 324 dan 81 ni ayirish.

$$5a^{4}+72a^{2}+243$$