13left(x-2yright)^2-8left(x-2yright)left(2x+yright)+7left(2x+yright)^2 eching

$$13 { \left(x-2y \right) }^{ 2 } -8 \left( x-2y \right) \left( 2x+y \right) +7 { \left(2x+y \right) }^{ 2 }$$

Baholash

$$25\left(x^{2}+3y^{2}\right)$$

Yechim qadamlari

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

$$13\left(x^{2}-4xy+4y^{2}\right)-8\left(x-2y\right)\left(2x+y\right)+7\left(2x+y\right)^{2}$$

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

$$13x^{2}-52xy+52y^{2}-8\left(x-2y\right)\left(2x+y\right)+7\left(2x+y\right)^{2}$$

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

$$13x^{2}-52xy+52y^{2}-8\left(x-2y\right)\left(2x+y\right)+7\left(4x^{2}+4xy+y^{2}\right)$$

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

$$13x^{2}-52xy+52y^{2}-8\left(x-2y\right)\left(2x+y\right)+28x^{2}+28xy+7y^{2}$$

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

$$13x^{2}-52xy+52y^{2}+\left(-8x+16y\right)\left(2x+y\right)+28x^{2}+28xy+7y^{2}$$

-8x+16y ga 2x+y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$13x^{2}-52xy+52y^{2}-16x^{2}+24xy+16y^{2}+28x^{2}+28xy+7y^{2}$$

-3x^{2} ni olish uchun 13x^{2} va -16x^{2} ni birlashtirish.

$$-3x^{2}-52xy+52y^{2}+24xy+16y^{2}+28x^{2}+28xy+7y^{2}$$

-28xy ni olish uchun -52xy va 24xy ni birlashtirish.

$$-3x^{2}-28xy+52y^{2}+16y^{2}+28x^{2}+28xy+7y^{2}$$

68y^{2} ni olish uchun 52y^{2} va 16y^{2} ni birlashtirish.

$$-3x^{2}-28xy+68y^{2}+28x^{2}+28xy+7y^{2}$$

25x^{2} ni olish uchun -3x^{2} va 28x^{2} ni birlashtirish.

$$25x^{2}-28xy+68y^{2}+28xy+7y^{2}$$

0 ni olish uchun -28xy va 28xy ni birlashtirish.

$$25x^{2}+68y^{2}+7y^{2}$$

75y^{2} ni olish uchun 68y^{2} va 7y^{2} ni birlashtirish.

$$25x^{2}+75y^{2}$$

Kengaytirish

$$25x^{2}+75y^{2}$$

Yechim qadamlari

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

$$13\left(x^{2}-4xy+4y^{2}\right)-8\left(x-2y\right)\left(2x+y\right)+7\left(2x+y\right)^{2}$$

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

$$13x^{2}-52xy+52y^{2}-8\left(x-2y\right)\left(2x+y\right)+7\left(2x+y\right)^{2}$$

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

$$13x^{2}-52xy+52y^{2}-8\left(x-2y\right)\left(2x+y\right)+7\left(4x^{2}+4xy+y^{2}\right)$$

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

$$13x^{2}-52xy+52y^{2}-8\left(x-2y\right)\left(2x+y\right)+28x^{2}+28xy+7y^{2}$$

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

$$13x^{2}-52xy+52y^{2}+\left(-8x+16y\right)\left(2x+y\right)+28x^{2}+28xy+7y^{2}$$

-8x+16y ga 2x+y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$13x^{2}-52xy+52y^{2}-16x^{2}+24xy+16y^{2}+28x^{2}+28xy+7y^{2}$$

-3x^{2} ni olish uchun 13x^{2} va -16x^{2} ni birlashtirish.

$$-3x^{2}-52xy+52y^{2}+24xy+16y^{2}+28x^{2}+28xy+7y^{2}$$

-28xy ni olish uchun -52xy va 24xy ni birlashtirish.

$$-3x^{2}-28xy+52y^{2}+16y^{2}+28x^{2}+28xy+7y^{2}$$

68y^{2} ni olish uchun 52y^{2} va 16y^{2} ni birlashtirish.

$$-3x^{2}-28xy+68y^{2}+28x^{2}+28xy+7y^{2}$$

25x^{2} ni olish uchun -3x^{2} va 28x^{2} ni birlashtirish.

$$25x^{2}-28xy+68y^{2}+28xy+7y^{2}$$

0 ni olish uchun -28xy va 28xy ni birlashtirish.

$$25x^{2}+68y^{2}+7y^{2}$$

75y^{2} ni olish uchun 68y^{2} va 7y^{2} ni birlashtirish.

$$25x^{2}+75y^{2}$$