(x-y)^2-8(x^2-y^2)+16(x+y)^2 eching

$$( x - y ) ^ { 2 } - 8 ( x ^ { 2 } - y ^ { 2 } ) + 16 ( x + y ) ^ { 2 }$$

Baholash

$$\left(3x+5y\right)^{2}$$

Yechim qadamlari

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

$$x^{2}-2xy+y^{2}-8\left(x^{2}-y^{2}\right)+16\left(x+y\right)^{2}$$

-8 ga x^{2}-y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-2xy+y^{2}-8x^{2}+8y^{2}+16\left(x+y\right)^{2}$$

-7x^{2} ni olish uchun x^{2} va -8x^{2} ni birlashtirish.

$$-7x^{2}-2xy+y^{2}+8y^{2}+16\left(x+y\right)^{2}$$

9y^{2} ni olish uchun y^{2} va 8y^{2} ni birlashtirish.

$$-7x^{2}-2xy+9y^{2}+16\left(x+y\right)^{2}$$

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

$$-7x^{2}-2xy+9y^{2}+16\left(x^{2}+2xy+y^{2}\right)$$

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

$$-7x^{2}-2xy+9y^{2}+16x^{2}+32xy+16y^{2}$$

9x^{2} ni olish uchun -7x^{2} va 16x^{2} ni birlashtirish.

$$9x^{2}-2xy+9y^{2}+32xy+16y^{2}$$

30xy ni olish uchun -2xy va 32xy ni birlashtirish.

$$9x^{2}+30xy+9y^{2}+16y^{2}$$

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

$$9x^{2}+30xy+25y^{2}$$

Kengaytirish

$$9x^{2}+30xy+25y^{2}$$

Yechim qadamlari

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

$$x^{2}-2xy+y^{2}-8\left(x^{2}-y^{2}\right)+16\left(x+y\right)^{2}$$

-8 ga x^{2}-y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-2xy+y^{2}-8x^{2}+8y^{2}+16\left(x+y\right)^{2}$$

-7x^{2} ni olish uchun x^{2} va -8x^{2} ni birlashtirish.

$$-7x^{2}-2xy+y^{2}+8y^{2}+16\left(x+y\right)^{2}$$

9y^{2} ni olish uchun y^{2} va 8y^{2} ni birlashtirish.

$$-7x^{2}-2xy+9y^{2}+16\left(x+y\right)^{2}$$

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

$$-7x^{2}-2xy+9y^{2}+16\left(x^{2}+2xy+y^{2}\right)$$

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

$$-7x^{2}-2xy+9y^{2}+16x^{2}+32xy+16y^{2}$$

9x^{2} ni olish uchun -7x^{2} va 16x^{2} ni birlashtirish.

$$9x^{2}-2xy+9y^{2}+32xy+16y^{2}$$

30xy ni olish uchun -2xy va 32xy ni birlashtirish.

$$9x^{2}+30xy+9y^{2}+16y^{2}$$

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

$$9x^{2}+30xy+25y^{2}$$