3(2x+5)^2-4(2x+5)(2x-5)+10(2x-5)^2= eching

$$3 ( 2 x + 5 ) ^ { 2 } - 4 ( 2 x + 5 ) ( 2 x - 5 ) + 10 ( 2 x - 5 ) ^ { 2 } =$$

Baholash

$$36x^{2}-140x+425$$

Yechim qadamlari

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

$$3\left(4x^{2}+20x+25\right)-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

3 ga 4x^{2}+20x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

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

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(4x^{2}-20x+25\right)$$

10 ga 4x^{2}-20x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+40x^{2}-200x+250$$

-4 ga 2x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x^{2}+60x+75+\left(-8x-20\right)\left(2x-5\right)+40x^{2}-200x+250$$

-8x-20 ga 2x-5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12x^{2}+60x+75-16x^{2}+100+40x^{2}-200x+250$$

-4x^{2} ni olish uchun 12x^{2} va -16x^{2} ni birlashtirish.

$$-4x^{2}+60x+75+100+40x^{2}-200x+250$$

175 olish uchun 75 va 100'ni qo'shing.

$$-4x^{2}+60x+175+40x^{2}-200x+250$$

36x^{2} ni olish uchun -4x^{2} va 40x^{2} ni birlashtirish.

$$36x^{2}+60x+175-200x+250$$

-140x ni olish uchun 60x va -200x ni birlashtirish.

$$36x^{2}-140x+175+250$$

425 olish uchun 175 va 250'ni qo'shing.

$$36x^{2}-140x+425$$

Kengaytirish

$$36x^{2}-140x+425$$

Yechim qadamlari

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

$$3\left(4x^{2}+20x+25\right)-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

3 ga 4x^{2}+20x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

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

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(4x^{2}-20x+25\right)$$

10 ga 4x^{2}-20x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+40x^{2}-200x+250$$

-4 ga 2x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x^{2}+60x+75+\left(-8x-20\right)\left(2x-5\right)+40x^{2}-200x+250$$

-8x-20 ga 2x-5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12x^{2}+60x+75-16x^{2}+100+40x^{2}-200x+250$$

-4x^{2} ni olish uchun 12x^{2} va -16x^{2} ni birlashtirish.

$$-4x^{2}+60x+75+100+40x^{2}-200x+250$$

175 olish uchun 75 va 100'ni qo'shing.

$$-4x^{2}+60x+175+40x^{2}-200x+250$$

36x^{2} ni olish uchun -4x^{2} va 40x^{2} ni birlashtirish.

$$36x^{2}+60x+175-200x+250$$

-140x ni olish uchun 60x va -200x ni birlashtirish.

$$36x^{2}-140x+175+250$$

425 olish uchun 175 va 250'ni qo'shing.

$$36x^{2}-140x+425$$