(2x+y)(2x-y)-(2x-y)^2 eching

$$( 2 x + y ) ( 2 x - y ) - ( 2 x - y ) ^ { 2 }$$

Baholash

$$2y\left(2x-y\right)$$

Yechim qadamlari

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

$$\left(2x\right)^{2}-y^{2}-\left(2x-y\right)^{2}$$

\left(2x\right)^{2} ni kengaytirish.

$$2^{2}x^{2}-y^{2}-\left(2x-y\right)^{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$4x^{2}-y^{2}-\left(2x-y\right)^{2}$$

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

$$4x^{2}-y^{2}-\left(4x^{2}-4xy+y^{2}\right)$$

4x^{2}-4xy+y^{2} teskarisini topish uchun har birining teskarisini toping.

$$4x^{2}-y^{2}-4x^{2}+4xy-y^{2}$$

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

$$-y^{2}+4xy-y^{2}$$

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

$$-2y^{2}+4xy$$

Kengaytirish

$$4xy-2y^{2}$$

Yechim qadamlari

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

$$\left(2x\right)^{2}-y^{2}-\left(2x-y\right)^{2}$$

\left(2x\right)^{2} ni kengaytirish.

$$2^{2}x^{2}-y^{2}-\left(2x-y\right)^{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$4x^{2}-y^{2}-\left(2x-y\right)^{2}$$

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

$$4x^{2}-y^{2}-\left(4x^{2}-4xy+y^{2}\right)$$

4x^{2}-4xy+y^{2} teskarisini topish uchun har birining teskarisini toping.

$$4x^{2}-y^{2}-4x^{2}+4xy-y^{2}$$

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

$$-y^{2}+4xy-y^{2}$$

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

$$-2y^{2}+4xy$$