25left(x-yright)^2-9left(x+yright)^2 eching

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

Baholash

$$4\left(x-4y\right)\left(4x-y\right)$$

Yechim qadamlari

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

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

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

$$25x^{2}-50xy+25y^{2}-9\left(x+y\right)^{2}$$

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

$$25x^{2}-50xy+25y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$25x^{2}-50xy+25y^{2}-9x^{2}-18xy-9y^{2}$$

16x^{2} ni olish uchun 25x^{2} va -9x^{2} ni birlashtirish.

$$16x^{2}-50xy+25y^{2}-18xy-9y^{2}$$

-68xy ni olish uchun -50xy va -18xy ni birlashtirish.

$$16x^{2}-68xy+25y^{2}-9y^{2}$$

16y^{2} ni olish uchun 25y^{2} va -9y^{2} ni birlashtirish.

$$16x^{2}-68xy+16y^{2}$$

Kengaytirish

$$16x^{2}-68xy+16y^{2}$$

Yechim qadamlari

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

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

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

$$25x^{2}-50xy+25y^{2}-9\left(x+y\right)^{2}$$

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

$$25x^{2}-50xy+25y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$25x^{2}-50xy+25y^{2}-9x^{2}-18xy-9y^{2}$$

16x^{2} ni olish uchun 25x^{2} va -9x^{2} ni birlashtirish.

$$16x^{2}-50xy+25y^{2}-18xy-9y^{2}$$

-68xy ni olish uchun -50xy va -18xy ni birlashtirish.

$$16x^{2}-68xy+25y^{2}-9y^{2}$$

16y^{2} ni olish uchun 25y^{2} va -9y^{2} ni birlashtirish.

$$16x^{2}-68xy+16y^{2}$$