4(3x-5y)^2-(4x-y)(x+y)+(2x+y)(2x-y) eching

$$4 ( 3 x - 5 y ) ^ { 2 } - ( 4 x - y ) ( x + y ) + ( 2 x + y ) ( 2 x - y )$$

Baholash

$$\left(3x-4y\right)\left(12x-25y\right)$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-5y\right)^{2} kengaytirilishi uchun ishlating.

$$4\left(9x^{2}-30xy+25y^{2}\right)-\left(4x-y\right)\left(x+y\right)+\left(2x+y\right)\left(2x-y\right)$$

4 ga 9x^{2}-30xy+25y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36x^{2}-120xy+100y^{2}-\left(4x-y\right)\left(x+y\right)+\left(2x+y\right)\left(2x-y\right)$$

4x-y ga x+y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$36x^{2}-120xy+100y^{2}-\left(4x^{2}+3xy-y^{2}\right)+\left(2x+y\right)\left(2x-y\right)$$

4x^{2}+3xy-y^{2} teskarisini topish uchun har birining teskarisini toping.

$$36x^{2}-120xy+100y^{2}-4x^{2}-3xy+y^{2}+\left(2x+y\right)\left(2x-y\right)$$

32x^{2} ni olish uchun 36x^{2} va -4x^{2} ni birlashtirish.

$$32x^{2}-120xy+100y^{2}-3xy+y^{2}+\left(2x+y\right)\left(2x-y\right)$$

-123xy ni olish uchun -120xy va -3xy ni birlashtirish.

$$32x^{2}-123xy+100y^{2}+y^{2}+\left(2x+y\right)\left(2x-y\right)$$

101y^{2} ni olish uchun 100y^{2} va y^{2} ni birlashtirish.

$$32x^{2}-123xy+101y^{2}+\left(2x+y\right)\left(2x-y\right)$$

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}.

$$32x^{2}-123xy+101y^{2}+\left(2x\right)^{2}-y^{2}$$

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

$$32x^{2}-123xy+101y^{2}+2^{2}x^{2}-y^{2}$$

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

$$32x^{2}-123xy+101y^{2}+4x^{2}-y^{2}$$

36x^{2} ni olish uchun 32x^{2} va 4x^{2} ni birlashtirish.

$$36x^{2}-123xy+101y^{2}-y^{2}$$

100y^{2} ni olish uchun 101y^{2} va -y^{2} ni birlashtirish.

$$36x^{2}-123xy+100y^{2}$$

Kengaytirish

$$36x^{2}-123xy+100y^{2}$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-5y\right)^{2} kengaytirilishi uchun ishlating.

$$4\left(9x^{2}-30xy+25y^{2}\right)-\left(4x-y\right)\left(x+y\right)+\left(2x+y\right)\left(2x-y\right)$$

4 ga 9x^{2}-30xy+25y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36x^{2}-120xy+100y^{2}-\left(4x-y\right)\left(x+y\right)+\left(2x+y\right)\left(2x-y\right)$$

4x-y ga x+y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$36x^{2}-120xy+100y^{2}-\left(4x^{2}+3xy-y^{2}\right)+\left(2x+y\right)\left(2x-y\right)$$

4x^{2}+3xy-y^{2} teskarisini topish uchun har birining teskarisini toping.

$$36x^{2}-120xy+100y^{2}-4x^{2}-3xy+y^{2}+\left(2x+y\right)\left(2x-y\right)$$

32x^{2} ni olish uchun 36x^{2} va -4x^{2} ni birlashtirish.

$$32x^{2}-120xy+100y^{2}-3xy+y^{2}+\left(2x+y\right)\left(2x-y\right)$$

-123xy ni olish uchun -120xy va -3xy ni birlashtirish.

$$32x^{2}-123xy+100y^{2}+y^{2}+\left(2x+y\right)\left(2x-y\right)$$

101y^{2} ni olish uchun 100y^{2} va y^{2} ni birlashtirish.

$$32x^{2}-123xy+101y^{2}+\left(2x+y\right)\left(2x-y\right)$$

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}.

$$32x^{2}-123xy+101y^{2}+\left(2x\right)^{2}-y^{2}$$

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

$$32x^{2}-123xy+101y^{2}+2^{2}x^{2}-y^{2}$$

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

$$32x^{2}-123xy+101y^{2}+4x^{2}-y^{2}$$

36x^{2} ni olish uchun 32x^{2} va 4x^{2} ni birlashtirish.

$$36x^{2}-123xy+101y^{2}-y^{2}$$

100y^{2} ni olish uchun 101y^{2} va -y^{2} ni birlashtirish.

$$36x^{2}-123xy+100y^{2}$$