4(x-y)^2-9(x+y)^2 eching

$$4 ( x - y ) ^ { 2 } - 9 ( x + y ) ^ { 2 }$$

Baholash

$$-\left(x+5y\right)\left(5x+y\right)$$

Yechim qadamlari

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

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

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

$$4x^{2}-8xy+4y^{2}-9\left(x+y\right)^{2}$$

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

$$4x^{2}-8xy+4y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$4x^{2}-8xy+4y^{2}-9x^{2}-18xy-9y^{2}$$

-5x^{2} ni olish uchun 4x^{2} va -9x^{2} ni birlashtirish.

$$-5x^{2}-8xy+4y^{2}-18xy-9y^{2}$$

-26xy ni olish uchun -8xy va -18xy ni birlashtirish.

$$-5x^{2}-26xy+4y^{2}-9y^{2}$$

-5y^{2} ni olish uchun 4y^{2} va -9y^{2} ni birlashtirish.

$$-5x^{2}-26xy-5y^{2}$$

Kengaytirish

$$-5x^{2}-26xy-5y^{2}$$

Yechim qadamlari

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

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

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

$$4x^{2}-8xy+4y^{2}-9\left(x+y\right)^{2}$$

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

$$4x^{2}-8xy+4y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$4x^{2}-8xy+4y^{2}-9x^{2}-18xy-9y^{2}$$

-5x^{2} ni olish uchun 4x^{2} va -9x^{2} ni birlashtirish.

$$-5x^{2}-8xy+4y^{2}-18xy-9y^{2}$$

-26xy ni olish uchun -8xy va -18xy ni birlashtirish.

$$-5x^{2}-26xy+4y^{2}-9y^{2}$$

-5y^{2} ni olish uchun 4y^{2} va -9y^{2} ni birlashtirish.

$$-5x^{2}-26xy-5y^{2}$$