(1-1/2a)^2+8(a-1/4)^2+(3/2a+1)(3/2a-1)+5a eching

$$( 1 - \frac { 1 } { 2 } a ) ^ { 2 } + 8 ( a - \frac { 1 } { 4 } ) ^ { 2 } + ( \frac { 3 } { 2 } a + 1 ) ( \frac { 3 } { 2 } a - 1 ) + 5 a$$

Baholash

$$\frac{21a^{2}+1}{2}$$

Yechim qadamlari

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

$$1-a+\frac{1}{4}a^{2}+8\left(a-\frac{1}{4}\right)^{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-\frac{1}{4}\right)^{2} kengaytirilishi uchun ishlating.

$$1-a+\frac{1}{4}a^{2}+8\left(a^{2}-\frac{1}{2}a+\frac{1}{16}\right)+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

8 ga a^{2}-\frac{1}{2}a+\frac{1}{16} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1-a+\frac{1}{4}a^{2}+8a^{2}-4a+\frac{1}{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

\frac{33}{4}a^{2} ni olish uchun \frac{1}{4}a^{2} va 8a^{2} ni birlashtirish.

$$1-a+\frac{33}{4}a^{2}-4a+\frac{1}{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

-5a ni olish uchun -a va -4a ni birlashtirish.

$$1-5a+\frac{33}{4}a^{2}+\frac{1}{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

\frac{3}{2} olish uchun 1 va \frac{1}{2}'ni qo'shing.

$$\frac{3}{2}-5a+\frac{33}{4}a^{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

Hisoblang: \left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$\frac{3}{2}-5a+\frac{33}{4}a^{2}+\left(\frac{3}{2}a\right)^{2}-1+5a$$

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

$$\frac{3}{2}-5a+\frac{33}{4}a^{2}+\left(\frac{3}{2}\right)^{2}a^{2}-1+5a$$

2 daraja ko‘rsatkichini \frac{3}{2} ga hisoblang va \frac{9}{4} ni qiymatni oling.

$$\frac{3}{2}-5a+\frac{33}{4}a^{2}+\frac{9}{4}a^{2}-1+5a$$

\frac{21}{2}a^{2} ni olish uchun \frac{33}{4}a^{2} va \frac{9}{4}a^{2} ni birlashtirish.

$$\frac{3}{2}-5a+\frac{21}{2}a^{2}-1+5a$$

\frac{1}{2} olish uchun \frac{3}{2} dan 1 ni ayirish.

$$\frac{1}{2}-5a+\frac{21}{2}a^{2}+5a$$

0 ni olish uchun -5a va 5a ni birlashtirish.

$$\frac{1}{2}+\frac{21}{2}a^{2}$$

Kengaytirish

$$\frac{21a^{2}+1}{2}$$

Yechim qadamlari

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

$$1-a+\frac{1}{4}a^{2}+8\left(a-\frac{1}{4}\right)^{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-\frac{1}{4}\right)^{2} kengaytirilishi uchun ishlating.

$$1-a+\frac{1}{4}a^{2}+8\left(a^{2}-\frac{1}{2}a+\frac{1}{16}\right)+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

8 ga a^{2}-\frac{1}{2}a+\frac{1}{16} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1-a+\frac{1}{4}a^{2}+8a^{2}-4a+\frac{1}{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

\frac{33}{4}a^{2} ni olish uchun \frac{1}{4}a^{2} va 8a^{2} ni birlashtirish.

$$1-a+\frac{33}{4}a^{2}-4a+\frac{1}{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

-5a ni olish uchun -a va -4a ni birlashtirish.

$$1-5a+\frac{33}{4}a^{2}+\frac{1}{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

\frac{3}{2} olish uchun 1 va \frac{1}{2}'ni qo'shing.

$$\frac{3}{2}-5a+\frac{33}{4}a^{2}+\left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right)+5a$$

Hisoblang: \left(\frac{3}{2}a+1\right)\left(\frac{3}{2}a-1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$\frac{3}{2}-5a+\frac{33}{4}a^{2}+\left(\frac{3}{2}a\right)^{2}-1+5a$$

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

$$\frac{3}{2}-5a+\frac{33}{4}a^{2}+\left(\frac{3}{2}\right)^{2}a^{2}-1+5a$$

2 daraja ko‘rsatkichini \frac{3}{2} ga hisoblang va \frac{9}{4} ni qiymatni oling.

$$\frac{3}{2}-5a+\frac{33}{4}a^{2}+\frac{9}{4}a^{2}-1+5a$$

\frac{21}{2}a^{2} ni olish uchun \frac{33}{4}a^{2} va \frac{9}{4}a^{2} ni birlashtirish.

$$\frac{3}{2}-5a+\frac{21}{2}a^{2}-1+5a$$

\frac{1}{2} olish uchun \frac{3}{2} dan 1 ni ayirish.

$$\frac{1}{2}-5a+\frac{21}{2}a^{2}+5a$$

0 ni olish uchun -5a va 5a ni birlashtirish.

$$\frac{1}{2}+\frac{21}{2}a^{2}$$