(a^{2}+4ab+3b^2)^2-(a+b)(a-3b)(a-b)(a+3b)-4ab(2a^2+7ab+6b^2) eching

$$( a ^ { 2 } + 4 a b + 3 b ^ { 2 } ) ^ { 2 } - ( a + b ) ( a - 3 b ) ( a - b ) ( a + 3 b ) - 4 a b ( 2 a ^ { 2 } + 7 a b + 6 b ^ { 2 } )$$

Baholash

$$4\left(ab\right)^{2}$$

Yechim qadamlari

a^{2}+4ab+3b^{2} kvadratini chiqarish.

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-\left(a+b\right)\left(a-3b\right)\left(a-b\right)\left(a+3b\right)-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

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

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-\left(a^{2}-2ab-3b^{2}\right)\left(a-b\right)\left(a+3b\right)-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

a^{2}-2ab-3b^{2} ga a-b ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-\left(a^{3}-3a^{2}b-ab^{2}+3b^{3}\right)\left(a+3b\right)-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

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

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-\left(a^{4}-10a^{2}b^{2}+9b^{4}\right)-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

a^{4}-10a^{2}b^{2}+9b^{4} teskarisini topish uchun har birining teskarisini toping.

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-a^{4}+10a^{2}b^{2}-9b^{4}-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

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

$$22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}+10a^{2}b^{2}-9b^{4}-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

32a^{2}b^{2} ni olish uchun 22a^{2}b^{2} va 10a^{2}b^{2} ni birlashtirish.

$$32a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-9b^{4}-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

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

$$32a^{2}b^{2}+24ab^{3}+8ba^{3}-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

-4ab ga 2a^{2}+7ab+6b^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$32a^{2}b^{2}+24ab^{3}+8ba^{3}-8a^{3}b-28a^{2}b^{2}-24ab^{3}$$

0 ni olish uchun 8ba^{3} va -8a^{3}b ni birlashtirish.

$$32a^{2}b^{2}+24ab^{3}-28a^{2}b^{2}-24ab^{3}$$

4a^{2}b^{2} ni olish uchun 32a^{2}b^{2} va -28a^{2}b^{2} ni birlashtirish.

$$4a^{2}b^{2}+24ab^{3}-24ab^{3}$$

0 ni olish uchun 24ab^{3} va -24ab^{3} ni birlashtirish.

$$4a^{2}b^{2}$$

Kengaytirish

$$4\left(ab\right)^{2}$$

Yechim qadamlari

a^{2}+4ab+3b^{2} kvadratini chiqarish.

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-\left(a+b\right)\left(a-3b\right)\left(a-b\right)\left(a+3b\right)-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

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

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-\left(a^{2}-2ab-3b^{2}\right)\left(a-b\right)\left(a+3b\right)-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

a^{2}-2ab-3b^{2} ga a-b ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-\left(a^{3}-3a^{2}b-ab^{2}+3b^{3}\right)\left(a+3b\right)-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

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

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-\left(a^{4}-10a^{2}b^{2}+9b^{4}\right)-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

a^{4}-10a^{2}b^{2}+9b^{4} teskarisini topish uchun har birining teskarisini toping.

$$a^{4}+22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-a^{4}+10a^{2}b^{2}-9b^{4}-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

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

$$22a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}+10a^{2}b^{2}-9b^{4}-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

32a^{2}b^{2} ni olish uchun 22a^{2}b^{2} va 10a^{2}b^{2} ni birlashtirish.

$$32a^{2}b^{2}+24ab^{3}+9b^{4}+8ba^{3}-9b^{4}-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

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

$$32a^{2}b^{2}+24ab^{3}+8ba^{3}-4ab\left(2a^{2}+7ab+6b^{2}\right)$$

-4ab ga 2a^{2}+7ab+6b^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$32a^{2}b^{2}+24ab^{3}+8ba^{3}-8a^{3}b-28a^{2}b^{2}-24ab^{3}$$

0 ni olish uchun 8ba^{3} va -8a^{3}b ni birlashtirish.

$$32a^{2}b^{2}+24ab^{3}-28a^{2}b^{2}-24ab^{3}$$

4a^{2}b^{2} ni olish uchun 32a^{2}b^{2} va -28a^{2}b^{2} ni birlashtirish.

$$4a^{2}b^{2}+24ab^{3}-24ab^{3}$$

0 ni olish uchun 24ab^{3} va -24ab^{3} ni birlashtirish.

$$4a^{2}b^{2}$$