(3x+4/x^2)(9x^2+12+16/x) eching

$$( 3 x + \frac { 4 } { x ^ { 2 } } ) ( 9 x ^ { 2 } + 12 + \frac { 16 } { x } )$$

Baholash

$$\frac{\left(3x^{3}+4\right)\left(9x^{3}+12x+16\right)}{x^{3}}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3x ni \frac{x^{2}}{x^{2}} marotabaga ko'paytirish.

$$\left(\frac{3xx^{2}}{x^{2}}+\frac{4}{x^{2}}\right)\left(9x^{2}+12+\frac{16}{x}\right)$$

\frac{3xx^{2}}{x^{2}} va \frac{4}{x^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3xx^{2}+4}{x^{2}}\left(9x^{2}+12+\frac{16}{x}\right)$$

3xx^{2}+4 ichidagi ko‘paytirishlarni bajaring.

$$\frac{3x^{3}+4}{x^{2}}\left(9x^{2}+12+\frac{16}{x}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 9x^{2}+12 ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{3x^{3}+4}{x^{2}}\left(\frac{\left(9x^{2}+12\right)x}{x}+\frac{16}{x}\right)$$

\frac{\left(9x^{2}+12\right)x}{x} va \frac{16}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3x^{3}+4}{x^{2}}\times \frac{\left(9x^{2}+12\right)x+16}{x}$$

\left(9x^{2}+12\right)x+16 ichidagi ko‘paytirishlarni bajaring.

$$\frac{3x^{3}+4}{x^{2}}\times \frac{9x^{3}+12x+16}{x}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3x^{3}+4}{x^{2}} ni \frac{9x^{3}+12x+16}{x} ga ko‘paytiring.

$$\frac{\left(3x^{3}+4\right)\left(9x^{3}+12x+16\right)}{x^{2}x}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\frac{\left(3x^{3}+4\right)\left(9x^{3}+12x+16\right)}{x^{3}}$$

3x^{3}+4 ga 9x^{3}+12x+16 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{27x^{6}+36x^{4}+84x^{3}+48x+64}{x^{3}}$$

Kengaytirish

$$27x^{3}+36x+84+\frac{48}{x^{2}}+\frac{64}{x^{3}}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3x ni \frac{x^{2}}{x^{2}} marotabaga ko'paytirish.

$$\left(\frac{3xx^{2}}{x^{2}}+\frac{4}{x^{2}}\right)\left(9x^{2}+12+\frac{16}{x}\right)$$

\frac{3xx^{2}}{x^{2}} va \frac{4}{x^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3xx^{2}+4}{x^{2}}\left(9x^{2}+12+\frac{16}{x}\right)$$

3xx^{2}+4 ichidagi ko‘paytirishlarni bajaring.

$$\frac{3x^{3}+4}{x^{2}}\left(9x^{2}+12+\frac{16}{x}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 9x^{2}+12 ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{3x^{3}+4}{x^{2}}\left(\frac{\left(9x^{2}+12\right)x}{x}+\frac{16}{x}\right)$$

\frac{\left(9x^{2}+12\right)x}{x} va \frac{16}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3x^{3}+4}{x^{2}}\times \frac{\left(9x^{2}+12\right)x+16}{x}$$

\left(9x^{2}+12\right)x+16 ichidagi ko‘paytirishlarni bajaring.

$$\frac{3x^{3}+4}{x^{2}}\times \frac{9x^{3}+12x+16}{x}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3x^{3}+4}{x^{2}} ni \frac{9x^{3}+12x+16}{x} ga ko‘paytiring.

$$\frac{\left(3x^{3}+4\right)\left(9x^{3}+12x+16\right)}{x^{2}x}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\frac{\left(3x^{3}+4\right)\left(9x^{3}+12x+16\right)}{x^{3}}$$

3x^{3}+4 ga 9x^{3}+12x+16 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{27x^{6}+36x^{4}+84x^{3}+48x+64}{x^{3}}$$