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

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

Baholash

$$4ay+1$$

Yechim qadamlari

a+1+2y kvadratini chiqarish.

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

Hisoblang: \left(a-1\right)\left(a+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

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

a^{2}-1 teskarisini topish uchun har birining teskarisini toping.

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

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

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

2 olish uchun 1 va 1'ni qo'shing.

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

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(1+2y\right)^{2} kengaytirilishi uchun ishlating.

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

1+4y+4y^{2} teskarisini topish uchun har birining teskarisini toping.

$$4y^{2}+4ay+4y+2a+2-1-4y-4y^{2}-2a$$

1 olish uchun 2 dan 1 ni ayirish.

$$4y^{2}+4ay+4y+2a+1-4y-4y^{2}-2a$$

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

$$4y^{2}+4ay+2a+1-4y^{2}-2a$$

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

$$4ay+2a+1-2a$$

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

$$4ay+1$$

Kengaytirish

$$4ay+1$$

Yechim qadamlari

a+1+2y kvadratini chiqarish.

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

Hisoblang: \left(a-1\right)\left(a+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

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

a^{2}-1 teskarisini topish uchun har birining teskarisini toping.

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

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

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

2 olish uchun 1 va 1'ni qo'shing.

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

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(1+2y\right)^{2} kengaytirilishi uchun ishlating.

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

1+4y+4y^{2} teskarisini topish uchun har birining teskarisini toping.

$$4y^{2}+4ay+4y+2a+2-1-4y-4y^{2}-2a$$

1 olish uchun 2 dan 1 ni ayirish.

$$4y^{2}+4ay+4y+2a+1-4y-4y^{2}-2a$$

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

$$4y^{2}+4ay+2a+1-4y^{2}-2a$$

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

$$4ay+2a+1-2a$$

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

$$4ay+1$$