(a+y-2)(a+y+2)-(a-y)^2-4(ay-1)+1 eching

$$( a + y - 2 ) ( a + y + 2 ) - ( a - y ) ^ { 2 } - 4 ( a y - 1 ) + 1$$

Baholash

$$1$$

Yechim qadamlari

Hisoblang: \left(a+y-2\right)\left(a+y+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, bu yerda a=a+y va b=2. 2 kvadratini chiqarish.

$$\left(a+y\right)^{2}-4-\left(a-y\right)^{2}-4\left(ay-1\right)+1$$

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

$$a^{2}+2ay+y^{2}-4-\left(a-y\right)^{2}-4\left(ay-1\right)+1$$

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

$$a^{2}+2ay+y^{2}-4-\left(a^{2}-2ay+y^{2}\right)-4\left(ay-1\right)+1$$

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

$$a^{2}+2ay+y^{2}-4-a^{2}+2ay-y^{2}-4\left(ay-1\right)+1$$

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

$$2ay+y^{2}-4+2ay-y^{2}-4\left(ay-1\right)+1$$

4ay ni olish uchun 2ay va 2ay ni birlashtirish.

$$4ay+y^{2}-4-y^{2}-4\left(ay-1\right)+1$$

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

$$4ay-4-4\left(ay-1\right)+1$$

-4 ga ay-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4ay-4-4ay+4+1$$

0 ni olish uchun 4ay va -4ay ni birlashtirish.

$$-4+4+1$$

0 olish uchun -4 va 4'ni qo'shing.

$$1$$

Omil

$$1$$