(2p-3)^2-(p-4)(p+4)-2p(p+2) eching

$$( 2 p - 3 ) ^ { 2 } - ( p - 4 ) ( p + 4 ) - 2 p ( p + 2 )$$

Baholash

$$\left(p-8\right)^{2}-39$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2p-3\right)^{2} kengaytirilishi uchun ishlating.

$$4p^{2}-12p+9-\left(p-4\right)\left(p+4\right)-2p\left(p+2\right)$$

Hisoblang: \left(p-4\right)\left(p+4\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 4 kvadratini chiqarish.

$$4p^{2}-12p+9-\left(p^{2}-16\right)-2p\left(p+2\right)$$

p^{2}-16 teskarisini topish uchun har birining teskarisini toping.

$$4p^{2}-12p+9-p^{2}+16-2p\left(p+2\right)$$

3p^{2} ni olish uchun 4p^{2} va -p^{2} ni birlashtirish.

$$3p^{2}-12p+9+16-2p\left(p+2\right)$$

25 olish uchun 9 va 16'ni qo'shing.

$$3p^{2}-12p+25-2p\left(p+2\right)$$

-2p ga p+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3p^{2}-12p+25-2p^{2}-4p$$

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

$$p^{2}-12p+25-4p$$

-16p ni olish uchun -12p va -4p ni birlashtirish.

$$p^{2}-16p+25$$

Kengaytirish

$$p^{2}-16p+25$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2p-3\right)^{2} kengaytirilishi uchun ishlating.

$$4p^{2}-12p+9-\left(p-4\right)\left(p+4\right)-2p\left(p+2\right)$$

Hisoblang: \left(p-4\right)\left(p+4\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 4 kvadratini chiqarish.

$$4p^{2}-12p+9-\left(p^{2}-16\right)-2p\left(p+2\right)$$

p^{2}-16 teskarisini topish uchun har birining teskarisini toping.

$$4p^{2}-12p+9-p^{2}+16-2p\left(p+2\right)$$

3p^{2} ni olish uchun 4p^{2} va -p^{2} ni birlashtirish.

$$3p^{2}-12p+9+16-2p\left(p+2\right)$$

25 olish uchun 9 va 16'ni qo'shing.

$$3p^{2}-12p+25-2p\left(p+2\right)$$

-2p ga p+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3p^{2}-12p+25-2p^{2}-4p$$

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

$$p^{2}-12p+25-4p$$

-16p ni olish uchun -12p va -4p ni birlashtirish.

$$p^{2}-16p+25$$