Giải thích các bước giải:
Ta có :
$(3a^2.b.c^2).(-2a^3.b^5.c).(-3a^5.b^2.c^2)$
$=3b\left(ac\right)^2\left(-2a^3b^5c\right)\left(-3a^5b^2c^2\right)$
$=\left(ac\right)^2b\cdot \:2a^3b^5c\cdot \:3a^5b^2c^2$
$=3\cdot \:2\cdot \:3a^5a^3b^5bc\left(abcc\right)^2$
$=3\cdot \:2\cdot \:3a^5a^3b^5bc\left(abc^2\right)^2$
$=3a^2b^2c^4b\cdot \:2a^3b^5c\cdot \:3a^5$
$=a^2b^2c^4b\cdot \:2a^3b^5c\cdot \:3^{1+1}a^5$
$=a^2b^2c^4b\cdot \:2a^3b^5c\cdot \:3^2a^5$
$=b^2c^4b\cdot \:2b^5c\cdot \:3^2a^{2+3+5}$
$=b^2c^4b\cdot \:2b^5c\cdot \:3^2a^{10}$
$=c^4\cdot \:2b^{2+1+5}c\cdot \:3^2a^{10}$
$=c^4\cdot \:2b^8c\cdot \:3^2a^{10}$
$=2b^8c^{4+1}\cdot \:3^2a^{10}$
$=18a^{10}b^8c^5$
$\to$ nếu $c>0\to 18a^{10}b^8c^5>0$
$\to (3a^2.b.c^2).(-2a^3.b^5.c).(-3a^5.b^2.c^2)>0$
$\to (3a^2.b.c^2),(-2a^3.b^5.c),(-3a^5.b^2.c^2)$ không cùng âm
