left(2x-3right)^2-(5x+3)*(3-5x)-(2-4x)*(4+2x) eching

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

Baholash

$$37x^{2}-8$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-3\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-12x+9-\left(5x+3\right)\left(3-5x\right)-\left(2-4x\right)\left(4+2x\right)$$

Hisoblang: \left(5x+3\right)\left(3-5x\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$4x^{2}-12x+9-\left(9-\left(5x\right)^{2}\right)-\left(2-4x\right)\left(4+2x\right)$$

\left(5x\right)^{2} ni kengaytirish.

$$4x^{2}-12x+9-\left(9-5^{2}x^{2}\right)-\left(2-4x\right)\left(4+2x\right)$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$4x^{2}-12x+9-\left(9-25x^{2}\right)-\left(2-4x\right)\left(4+2x\right)$$

9-25x^{2} teskarisini topish uchun har birining teskarisini toping.

$$4x^{2}-12x+9-9+25x^{2}-\left(2-4x\right)\left(4+2x\right)$$

0 olish uchun 9 dan 9 ni ayirish.

$$4x^{2}-12x+25x^{2}-\left(2-4x\right)\left(4+2x\right)$$

29x^{2} ni olish uchun 4x^{2} va 25x^{2} ni birlashtirish.

$$29x^{2}-12x-\left(2-4x\right)\left(4+2x\right)$$

2-4x ga 4+2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$29x^{2}-12x-\left(8-12x-8x^{2}\right)$$

8-12x-8x^{2} teskarisini topish uchun har birining teskarisini toping.

$$29x^{2}-12x-8+12x+8x^{2}$$

0 ni olish uchun -12x va 12x ni birlashtirish.

$$29x^{2}-8+8x^{2}$$

37x^{2} ni olish uchun 29x^{2} va 8x^{2} ni birlashtirish.

$$37x^{2}-8$$

Kengaytirish

$$37x^{2}-8$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-3\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-12x+9-\left(5x+3\right)\left(3-5x\right)-\left(2-4x\right)\left(4+2x\right)$$

Hisoblang: \left(5x+3\right)\left(3-5x\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$4x^{2}-12x+9-\left(9-\left(5x\right)^{2}\right)-\left(2-4x\right)\left(4+2x\right)$$

\left(5x\right)^{2} ni kengaytirish.

$$4x^{2}-12x+9-\left(9-5^{2}x^{2}\right)-\left(2-4x\right)\left(4+2x\right)$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$4x^{2}-12x+9-\left(9-25x^{2}\right)-\left(2-4x\right)\left(4+2x\right)$$

9-25x^{2} teskarisini topish uchun har birining teskarisini toping.

$$4x^{2}-12x+9-9+25x^{2}-\left(2-4x\right)\left(4+2x\right)$$

0 olish uchun 9 dan 9 ni ayirish.

$$4x^{2}-12x+25x^{2}-\left(2-4x\right)\left(4+2x\right)$$

29x^{2} ni olish uchun 4x^{2} va 25x^{2} ni birlashtirish.

$$29x^{2}-12x-\left(2-4x\right)\left(4+2x\right)$$

2-4x ga 4+2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$29x^{2}-12x-\left(8-12x-8x^{2}\right)$$

8-12x-8x^{2} teskarisini topish uchun har birining teskarisini toping.

$$29x^{2}-12x-8+12x+8x^{2}$$

0 ni olish uchun -12x va 12x ni birlashtirish.

$$29x^{2}-8+8x^{2}$$

37x^{2} ni olish uchun 29x^{2} va 8x^{2} ni birlashtirish.

$$37x^{2}-8$$