(4a-5b)(4a+5b)-(4a+2b)(4a-3b)+(-5b)^2 eching

$$( 4 a - 5 b ) ( 4 a + 5 b ) - ( 4 a + 2 b ) ( 4 a - 3 b ) + ( - 5 b ) ^ { 2 }$$

Baholash

$$2b\left(2a+3b\right)$$

Yechim qadamlari

Hisoblang: \left(4a-5b\right)\left(4a+5b\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(4a\right)^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

\left(4a\right)^{2} ni kengaytirish.

$$4^{2}a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$16a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

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

$$16a^{2}-5^{2}b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

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

$$16a^{2}-25b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

4a+2b ga 4a-3b ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$16a^{2}-25b^{2}-\left(16a^{2}-4ab-6b^{2}\right)+\left(-5b\right)^{2}$$

16a^{2}-4ab-6b^{2} teskarisini topish uchun har birining teskarisini toping.

$$16a^{2}-25b^{2}-16a^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

0 ni olish uchun 16a^{2} va -16a^{2} ni birlashtirish.

$$-25b^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

-19b^{2} ni olish uchun -25b^{2} va 6b^{2} ni birlashtirish.

$$-19b^{2}+4ab+\left(-5b\right)^{2}$$

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

$$-19b^{2}+4ab+\left(-5\right)^{2}b^{2}$$

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

$$-19b^{2}+4ab+25b^{2}$$

6b^{2} ni olish uchun -19b^{2} va 25b^{2} ni birlashtirish.

$$6b^{2}+4ab$$

Kengaytirish

$$4ab+6b^{2}$$

Yechim qadamlari

Hisoblang: \left(4a-5b\right)\left(4a+5b\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(4a\right)^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

\left(4a\right)^{2} ni kengaytirish.

$$4^{2}a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$16a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

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

$$16a^{2}-5^{2}b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

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

$$16a^{2}-25b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

4a+2b ga 4a-3b ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$16a^{2}-25b^{2}-\left(16a^{2}-4ab-6b^{2}\right)+\left(-5b\right)^{2}$$

16a^{2}-4ab-6b^{2} teskarisini topish uchun har birining teskarisini toping.

$$16a^{2}-25b^{2}-16a^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

0 ni olish uchun 16a^{2} va -16a^{2} ni birlashtirish.

$$-25b^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

-19b^{2} ni olish uchun -25b^{2} va 6b^{2} ni birlashtirish.

$$-19b^{2}+4ab+\left(-5b\right)^{2}$$

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

$$-19b^{2}+4ab+\left(-5\right)^{2}b^{2}$$

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

$$-19b^{2}+4ab+25b^{2}$$

6b^{2} ni olish uchun -19b^{2} va 25b^{2} ni birlashtirish.

$$6b^{2}+4ab$$