15a^2+12a eching

$$15 a ^ { 2 } + 12 a$$

Omil

$$3a\left(5a+4\right)$$

Yechim qadamlari

3 omili.

$$3\left(5a^{2}+4a\right)$$

Hisoblang: 5a^{2}+4a. a omili.

$$a\left(5a+4\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$3a\left(5a+4\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$15a^{2}+12a=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$a=\frac{-12±\sqrt{12^{2}}}{2\times 15}$$

12^{2} ning kvadrat ildizini chiqarish.

$$a=\frac{-12±12}{2\times 15}$$

2 ni 15 marotabaga ko'paytirish.

$$a=\frac{-12±12}{30}$$

a=\frac{-12±12}{30} tenglamasini yeching, bunda ± musbat. -12 ni 12 ga qo'shish.

$$a=\frac{0}{30}$$

0 ni 30 ga bo'lish.

$$a=0$$

a=\frac{-12±12}{30} tenglamasini yeching, bunda ± manfiy. -12 dan 12 ni ayirish.

$$a=-\frac{24}{30}$$

\frac{-24}{30} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$a=-\frac{4}{5}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 0 ga va x_{2} uchun -\frac{4}{5} ga bo‘ling.

$$15a^{2}+12a=15a\left(a-\left(-\frac{4}{5}\right)\right)$$

p-\left(-q\right) shaklining barcha amallarigani p+q ga soddalashtiring.

$$15a^{2}+12a=15a\left(a+\frac{4}{5}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{4}{5} ni a ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$15a^{2}+12a=15a\times \frac{5a+4}{5}$$

15 va 5 ichida eng katta umumiy 5 faktorini bekor qiling.

$$15a^{2}+12a=3a\left(5a+4\right)$$

Baholash

$$3a\left(5a+4\right)$$