3(x+2)^2-(x+4)^2 eching

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

Baholash

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

Yechim qadamlari

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

$$3\left(x^{2}+4x+4\right)-\left(x+4\right)^{2}$$

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

$$3x^{2}+12x+12-\left(x+4\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+4\right)^{2} kengaytirilishi uchun ishlating.

$$3x^{2}+12x+12-\left(x^{2}+8x+16\right)$$

x^{2}+8x+16 teskarisini topish uchun har birining teskarisini toping.

$$3x^{2}+12x+12-x^{2}-8x-16$$

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

$$2x^{2}+12x+12-8x-16$$

4x ni olish uchun 12x va -8x ni birlashtirish.

$$2x^{2}+4x+12-16$$

-4 olish uchun 12 dan 16 ni ayirish.

$$2x^{2}+4x-4$$

Kengaytirish

$$2x^{2}+4x-4$$

Yechim qadamlari

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

$$3\left(x^{2}+4x+4\right)-\left(x+4\right)^{2}$$

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

$$3x^{2}+12x+12-\left(x+4\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+4\right)^{2} kengaytirilishi uchun ishlating.

$$3x^{2}+12x+12-\left(x^{2}+8x+16\right)$$

x^{2}+8x+16 teskarisini topish uchun har birining teskarisini toping.

$$3x^{2}+12x+12-x^{2}-8x-16$$

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

$$2x^{2}+12x+12-8x-16$$

4x ni olish uchun 12x va -8x ni birlashtirish.

$$2x^{2}+4x+12-16$$

-4 olish uchun 12 dan 16 ni ayirish.

$$2x^{2}+4x-4$$