[1/2x^2+1/4(1/2x-2)(x^2+4x-16)-(1/2x+2)+(x+3)^2]*[4x+9] eching

$$[ \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 4 } ( \frac { 1 } { 2 } x - 2 ) ( x ^ { 2 } + 4 x - 16 ) - ( \frac { 1 } { 2 } x + 2 ) + ( x + 3 ) ^ { 2 } ] \cdot [ 4 x + 9 ]$$

Baholash

$$\frac{\left(4x+9\right)\left(x^{3}+12x^{2}+12x+120\right)}{8}$$

Yechim qadamlari

\frac{1}{4} ga \frac{1}{2}x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(\frac{1}{2}x^{2}+\left(\frac{1}{8}x-\frac{1}{2}\right)\left(x^{2}+4x-16\right)-\left(\frac{1}{2}x+2\right)+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

\frac{1}{8}x-\frac{1}{2} ga x^{2}+4x-16 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-4x+8-\left(\frac{1}{2}x+2\right)+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

\frac{1}{2}x+2 teskarisini topish uchun har birining teskarisini toping.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-4x+8-\frac{1}{2}x-2+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

-\frac{9}{2}x ni olish uchun -4x va -\frac{1}{2}x ni birlashtirish.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+8-2+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

6 olish uchun 8 dan 2 ni ayirish.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

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

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+x^{2}+6x+9\right)\left(4x+9\right)$$

\frac{3}{2}x^{2} ni olish uchun \frac{1}{2}x^{2} va x^{2} ni birlashtirish.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+6x+9\right)\left(4x+9\right)$$

\frac{3}{2}x ni olish uchun -\frac{9}{2}x va 6x ni birlashtirish.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+6+9\right)\left(4x+9\right)$$

15 olish uchun 6 va 9'ni qo'shing.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+15\right)\left(4x+9\right)$$

\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+15 ga 4x+9 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{57}{8}x^{3}+\frac{39}{2}x^{2}+\frac{1}{2}x^{4}+\frac{147}{2}x+135$$

Kengaytirish

$$\frac{x^{4}}{2}+\frac{57x^{3}}{8}+\frac{39x^{2}}{2}+\frac{147x}{2}+135$$

Yechim qadamlari

\frac{1}{4} ga \frac{1}{2}x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(\frac{1}{2}x^{2}+\left(\frac{1}{8}x-\frac{1}{2}\right)\left(x^{2}+4x-16\right)-\left(\frac{1}{2}x+2\right)+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

\frac{1}{8}x-\frac{1}{2} ga x^{2}+4x-16 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-4x+8-\left(\frac{1}{2}x+2\right)+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

\frac{1}{2}x+2 teskarisini topish uchun har birining teskarisini toping.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-4x+8-\frac{1}{2}x-2+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

-\frac{9}{2}x ni olish uchun -4x va -\frac{1}{2}x ni birlashtirish.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+8-2+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

6 olish uchun 8 dan 2 ni ayirish.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

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

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+x^{2}+6x+9\right)\left(4x+9\right)$$

\frac{3}{2}x^{2} ni olish uchun \frac{1}{2}x^{2} va x^{2} ni birlashtirish.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+6x+9\right)\left(4x+9\right)$$

\frac{3}{2}x ni olish uchun -\frac{9}{2}x va 6x ni birlashtirish.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+6+9\right)\left(4x+9\right)$$

15 olish uchun 6 va 9'ni qo'shing.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+15\right)\left(4x+9\right)$$

\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+15 ga 4x+9 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{57}{8}x^{3}+\frac{39}{2}x^{2}+\frac{1}{2}x^{4}+\frac{147}{2}x+135$$