(5/2-r/3)(5/2+r/3) eching

$$( \frac { 5 } { 2 } - \frac { r } { 3 } ) ( \frac { 5 } { 2 } + \frac { r } { 3 } )$$

Baholash

$$-\frac{r^{2}}{9}+\frac{25}{4}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 va 3 ning eng kichik umumiy karralisi 6. \frac{5}{2} ni \frac{3}{3} marotabaga ko'paytirish. \frac{r}{3} ni \frac{2}{2} marotabaga ko'paytirish.

$$\left(\frac{5\times 3}{6}-\frac{2r}{6}\right)\left(\frac{5}{2}+\frac{r}{3}\right)$$

\frac{5\times 3}{6} va \frac{2r}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{5\times 3-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

5\times 3-2r ichidagi ko‘paytirishlarni bajaring.

$$\frac{15-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 va 3 ning eng kichik umumiy karralisi 6. \frac{5}{2} ni \frac{3}{3} marotabaga ko'paytirish. \frac{r}{3} ni \frac{2}{2} marotabaga ko'paytirish.

$$\frac{15-2r}{6}\left(\frac{5\times 3}{6}+\frac{2r}{6}\right)$$

\frac{5\times 3}{6} va \frac{2r}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{15-2r}{6}\times \frac{5\times 3+2r}{6}$$

5\times 3+2r ichidagi ko‘paytirishlarni bajaring.

$$\frac{15-2r}{6}\times \frac{15+2r}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{15-2r}{6} ni \frac{15+2r}{6} ga ko‘paytiring.

$$\frac{\left(15-2r\right)\left(15+2r\right)}{6\times 6}$$

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

$$\frac{\left(15-2r\right)\left(15+2r\right)}{36}$$

Hisoblang: \left(15-2r\right)\left(15+2r\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{15^{2}-\left(2r\right)^{2}}{36}$$

2 daraja ko‘rsatkichini 15 ga hisoblang va 225 ni qiymatni oling.

$$\frac{225-\left(2r\right)^{2}}{36}$$

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

$$\frac{225-2^{2}r^{2}}{36}$$

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

$$\frac{225-4r^{2}}{36}$$

Kengaytirish

$$-\frac{r^{2}}{9}+\frac{25}{4}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 va 3 ning eng kichik umumiy karralisi 6. \frac{5}{2} ni \frac{3}{3} marotabaga ko'paytirish. \frac{r}{3} ni \frac{2}{2} marotabaga ko'paytirish.

$$\left(\frac{5\times 3}{6}-\frac{2r}{6}\right)\left(\frac{5}{2}+\frac{r}{3}\right)$$

\frac{5\times 3}{6} va \frac{2r}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{5\times 3-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

5\times 3-2r ichidagi ko‘paytirishlarni bajaring.

$$\frac{15-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 va 3 ning eng kichik umumiy karralisi 6. \frac{5}{2} ni \frac{3}{3} marotabaga ko'paytirish. \frac{r}{3} ni \frac{2}{2} marotabaga ko'paytirish.

$$\frac{15-2r}{6}\left(\frac{5\times 3}{6}+\frac{2r}{6}\right)$$

\frac{5\times 3}{6} va \frac{2r}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{15-2r}{6}\times \frac{5\times 3+2r}{6}$$

5\times 3+2r ichidagi ko‘paytirishlarni bajaring.

$$\frac{15-2r}{6}\times \frac{15+2r}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{15-2r}{6} ni \frac{15+2r}{6} ga ko‘paytiring.

$$\frac{\left(15-2r\right)\left(15+2r\right)}{6\times 6}$$

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

$$\frac{\left(15-2r\right)\left(15+2r\right)}{36}$$

Hisoblang: \left(15-2r\right)\left(15+2r\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{15^{2}-\left(2r\right)^{2}}{36}$$

2 daraja ko‘rsatkichini 15 ga hisoblang va 225 ni qiymatni oling.

$$\frac{225-\left(2r\right)^{2}}{36}$$

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

$$\frac{225-2^{2}r^{2}}{36}$$

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

$$\frac{225-4r^{2}}{36}$$