(3x-2)(3x+2)-(2x-5)^2 eching

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

Baholash

$$5x^{2}+20x-29$$

Yechim qadamlari

Hisoblang: \left(3x-2\right)\left(3x+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 2 kvadratini chiqarish.

$$\left(3x\right)^{2}-4-\left(2x-5\right)^{2}$$

\left(3x\right)^{2} ni kengaytirish.

$$3^{2}x^{2}-4-\left(2x-5\right)^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$9x^{2}-4-\left(2x-5\right)^{2}$$

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

$$9x^{2}-4-\left(4x^{2}-20x+25\right)$$

4x^{2}-20x+25 teskarisini topish uchun har birining teskarisini toping.

$$9x^{2}-4-4x^{2}+20x-25$$

5x^{2} ni olish uchun 9x^{2} va -4x^{2} ni birlashtirish.

$$5x^{2}-4+20x-25$$

-29 olish uchun -4 dan 25 ni ayirish.

$$5x^{2}-29+20x$$

Kengaytirish

$$5x^{2}+20x-29$$

Yechim qadamlari

Hisoblang: \left(3x-2\right)\left(3x+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 2 kvadratini chiqarish.

$$\left(3x\right)^{2}-4-\left(2x-5\right)^{2}$$

\left(3x\right)^{2} ni kengaytirish.

$$3^{2}x^{2}-4-\left(2x-5\right)^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$9x^{2}-4-\left(2x-5\right)^{2}$$

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

$$9x^{2}-4-\left(4x^{2}-20x+25\right)$$

4x^{2}-20x+25 teskarisini topish uchun har birining teskarisini toping.

$$9x^{2}-4-4x^{2}+20x-25$$

5x^{2} ni olish uchun 9x^{2} va -4x^{2} ni birlashtirish.

$$5x^{2}-4+20x-25$$

-29 olish uchun -4 dan 25 ni ayirish.

$$5x^{2}-29+20x$$