(a+b)^2-[(a-b)^2+(a+b)(a-b)-4a(a-b)]-(3a^2+b^2) eching

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

Baholash

$$0$$

Yechim qadamlari

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

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

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

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

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

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

2a^{2} ni olish uchun a^{2} va a^{2} ni birlashtirish.

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

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

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

3a^{2}+b^{2} teskarisini topish uchun har birining teskarisini toping.

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

-4a ga a-b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

2ab ni olish uchun -2ab va 4ab ni birlashtirish.

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

-2a^{2}+2ab teskarisini topish uchun har birining teskarisini toping.

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

3a^{2} ni olish uchun a^{2} va 2a^{2} ni birlashtirish.

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

0 ni olish uchun 2ab va -2ab ni birlashtirish.

$$3a^{2}+b^{2}-3a^{2}-b^{2}$$

0 ni olish uchun 3a^{2} va -3a^{2} ni birlashtirish.

$$b^{2}-b^{2}$$

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

$$0$$

Omil

$$0$$