(2a+1)^3-2a(2a+1)^2-(2a)^2-1 eching

$$( 2 a + 1 ) ^ { 3 } - 2 a ( 2 a + 1 ) ^ { 2 } - ( 2 a ) ^ { 2 } - 1$$

Baholash

$$4a$$

Yechim qadamlari

\left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} binom teoremasini \left(2a+1\right)^{3} kengaytirilishi uchun ishlating.

$$8a^{3}+12a^{2}+6a+1-2a\left(2a+1\right)^{2}-\left(2a\right)^{2}-1$$

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(2a+1\right)^{2} kengaytirilishi uchun ishlating.

$$8a^{3}+12a^{2}+6a+1-2a\left(4a^{2}+4a+1\right)-\left(2a\right)^{2}-1$$

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

$$8a^{3}+12a^{2}+6a+1-2a\left(4a^{2}+4a+1\right)-2^{2}a^{2}-1$$

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

$$8a^{3}+12a^{2}+6a+1-2a\left(4a^{2}+4a+1\right)-4a^{2}-1$$

-2a ga 4a^{2}+4a+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8a^{3}+12a^{2}+6a+1-8a^{3}-8a^{2}-2a-4a^{2}-1$$

0 ni olish uchun 8a^{3} va -8a^{3} ni birlashtirish.

$$12a^{2}+6a+1-8a^{2}-2a-4a^{2}-1$$

4a^{2} ni olish uchun 12a^{2} va -8a^{2} ni birlashtirish.

$$4a^{2}+6a+1-2a-4a^{2}-1$$

4a ni olish uchun 6a va -2a ni birlashtirish.

$$4a^{2}+4a+1-4a^{2}-1$$

0 ni olish uchun 4a^{2} va -4a^{2} ni birlashtirish.

$$4a+1-1$$

0 olish uchun 1 dan 1 ni ayirish.

$$4a$$

Kengaytirish

$$4a$$

Yechim qadamlari

\left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} binom teoremasini \left(2a+1\right)^{3} kengaytirilishi uchun ishlating.

$$8a^{3}+12a^{2}+6a+1-2a\left(2a+1\right)^{2}-\left(2a\right)^{2}-1$$

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(2a+1\right)^{2} kengaytirilishi uchun ishlating.

$$8a^{3}+12a^{2}+6a+1-2a\left(4a^{2}+4a+1\right)-\left(2a\right)^{2}-1$$

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

$$8a^{3}+12a^{2}+6a+1-2a\left(4a^{2}+4a+1\right)-2^{2}a^{2}-1$$

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

$$8a^{3}+12a^{2}+6a+1-2a\left(4a^{2}+4a+1\right)-4a^{2}-1$$

-2a ga 4a^{2}+4a+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8a^{3}+12a^{2}+6a+1-8a^{3}-8a^{2}-2a-4a^{2}-1$$

0 ni olish uchun 8a^{3} va -8a^{3} ni birlashtirish.

$$12a^{2}+6a+1-8a^{2}-2a-4a^{2}-1$$

4a^{2} ni olish uchun 12a^{2} va -8a^{2} ni birlashtirish.

$$4a^{2}+6a+1-2a-4a^{2}-1$$

4a ni olish uchun 6a va -2a ni birlashtirish.

$$4a^{2}+4a+1-4a^{2}-1$$

0 ni olish uchun 4a^{2} va -4a^{2} ni birlashtirish.

$$4a+1-1$$

0 olish uchun 1 dan 1 ni ayirish.

$$4a$$