-(9x+6)^2+(3x+7)(3x-7) eching

$$- ( 9 x + 6 ) ^ { 2 } + ( 3 x + 7 ) ( 3 x - 7 )$$

Baholash

$$-72x^{2}-108x-85$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(9x+6\right)^{2} kengaytirilishi uchun ishlating.

$$-\left(81x^{2}+108x+36\right)+\left(3x+7\right)\left(3x-7\right)$$

81x^{2}+108x+36 teskarisini topish uchun har birining teskarisini toping.

$$-81x^{2}-108x-36+\left(3x+7\right)\left(3x-7\right)$$

Hisoblang: \left(3x+7\right)\left(3x-7\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 7 kvadratini chiqarish.

$$-81x^{2}-108x-36+\left(3x\right)^{2}-49$$

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

$$-81x^{2}-108x-36+3^{2}x^{2}-49$$

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

$$-81x^{2}-108x-36+9x^{2}-49$$

-72x^{2} ni olish uchun -81x^{2} va 9x^{2} ni birlashtirish.

$$-72x^{2}-108x-36-49$$

-85 olish uchun -36 dan 49 ni ayirish.

$$-72x^{2}-108x-85$$

Kengaytirish

$$-72x^{2}-108x-85$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(9x+6\right)^{2} kengaytirilishi uchun ishlating.

$$-\left(81x^{2}+108x+36\right)+\left(3x+7\right)\left(3x-7\right)$$

81x^{2}+108x+36 teskarisini topish uchun har birining teskarisini toping.

$$-81x^{2}-108x-36+\left(3x+7\right)\left(3x-7\right)$$

Hisoblang: \left(3x+7\right)\left(3x-7\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 7 kvadratini chiqarish.

$$-81x^{2}-108x-36+\left(3x\right)^{2}-49$$

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

$$-81x^{2}-108x-36+3^{2}x^{2}-49$$

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

$$-81x^{2}-108x-36+9x^{2}-49$$

-72x^{2} ni olish uchun -81x^{2} va 9x^{2} ni birlashtirish.

$$-72x^{2}-108x-36-49$$

-85 olish uchun -36 dan 49 ni ayirish.

$$-72x^{2}-108x-85$$