(1/3+x/2)(1/9-x^2/4)(frac{1}{3}-frac{x}{2}) eching

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

Baholash

$$\frac{\left(4-9x^{2}\right)^{2}}{1296}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 va 2 ning eng kichik umumiy karralisi 6. \frac{1}{3} ni \frac{2}{2} marotabaga ko'paytirish. \frac{x}{2} ni \frac{3}{3} marotabaga ko'paytirish.

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

\frac{2}{6} va \frac{3x}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 9 va 4 ning eng kichik umumiy karralisi 36. \frac{1}{9} ni \frac{4}{4} marotabaga ko'paytirish. \frac{x^{2}}{4} ni \frac{9}{9} marotabaga ko'paytirish.

$$\frac{2+3x}{6}\left(\frac{4}{36}-\frac{9x^{2}}{36}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

\frac{4}{36} va \frac{9x^{2}}{36} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{1}{3}-\frac{x}{2}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 va 2 ning eng kichik umumiy karralisi 6. \frac{1}{3} ni \frac{2}{2} marotabaga ko'paytirish. \frac{x}{2} ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{2}{6}-\frac{3x}{6}\right)$$

\frac{2}{6} va \frac{3x}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\times \frac{2-3x}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2+3x}{6} ni \frac{4-9x^{2}}{36} ga ko‘paytiring.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36}\times \frac{2-3x}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36} ni \frac{2-3x}{6} ga ko‘paytiring.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{6\times 36\times 6}$$

216 hosil qilish uchun 6 va 36 ni ko'paytirish.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{216\times 6}$$

1296 hosil qilish uchun 216 va 6 ni ko'paytirish.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{1296}$$

2+3x ga 4-9x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(8-18x^{2}+12x-27x^{3}\right)\left(2-3x\right)}{1296}$$

8-18x^{2}+12x-27x^{3} ga 2-3x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{16-72x^{2}+81x^{4}}{1296}$$

Kengaytirish

$$\frac{x^{4}}{16}-\frac{x^{2}}{18}+\frac{1}{81}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 va 2 ning eng kichik umumiy karralisi 6. \frac{1}{3} ni \frac{2}{2} marotabaga ko'paytirish. \frac{x}{2} ni \frac{3}{3} marotabaga ko'paytirish.

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

\frac{2}{6} va \frac{3x}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 9 va 4 ning eng kichik umumiy karralisi 36. \frac{1}{9} ni \frac{4}{4} marotabaga ko'paytirish. \frac{x^{2}}{4} ni \frac{9}{9} marotabaga ko'paytirish.

$$\frac{2+3x}{6}\left(\frac{4}{36}-\frac{9x^{2}}{36}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

\frac{4}{36} va \frac{9x^{2}}{36} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{1}{3}-\frac{x}{2}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 va 2 ning eng kichik umumiy karralisi 6. \frac{1}{3} ni \frac{2}{2} marotabaga ko'paytirish. \frac{x}{2} ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{2}{6}-\frac{3x}{6}\right)$$

\frac{2}{6} va \frac{3x}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\times \frac{2-3x}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2+3x}{6} ni \frac{4-9x^{2}}{36} ga ko‘paytiring.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36}\times \frac{2-3x}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36} ni \frac{2-3x}{6} ga ko‘paytiring.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{6\times 36\times 6}$$

216 hosil qilish uchun 6 va 36 ni ko'paytirish.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{216\times 6}$$

1296 hosil qilish uchun 216 va 6 ni ko'paytirish.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{1296}$$

2+3x ga 4-9x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(8-18x^{2}+12x-27x^{3}\right)\left(2-3x\right)}{1296}$$

8-18x^{2}+12x-27x^{3} ga 2-3x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{16-72x^{2}+81x^{4}}{1296}$$