(A-B)-(A²+ AB + B² 1 = A3 B3

pacal the great: the throne was passed on to pacal through a female; as a result, he believed that he must legitimize his claim to the throne to add stability to his reign.

as a result, the daughter of ac kan's brother ruled until her son, pacal, reached an age old enough to assume the throne.

pacal the great became the king of the mayan city of palenque in a different way than most mayan kings.

pacal pointed out that ac kan had succeeded his mother as ruler, thereby establishing a precedent for the rule to pass through a female.  

he tried to justify that the way he gained the throne by connecting his mother with the divine mother and the mythological events that happened during the creation of the world.  

typically, the son of a male mayan ruler inherited the throne, but in 612 ce, king ac kan died and did not leave behind a male heir.

montezuma 1: even so, these wars of conquest failed to provide enough human sacrifices and because of this, he formed a triple alliance with cities in the valley of puebla-tlascala.  

in addition, montezuma realized that his government failed to the aztecs during the famine.

in order to appease him, montezuma increased the number of human sacrifices.

the aztec performed human sacrifices to their god huitzilopotchli because they believed he desired human blood.  

around 1440 ce, montezuma i became the fifth emperor of the aztecs and went on to rule for 28 years.  

soon after he assumed the throne, the aztecs were hit with a series of disasters, namely a plague of locusts, a flood, and a harsh frost  

huayna capac: huayna capac also fought to gain territories north of his empire in what is now ecuador.  

huayna capac significantly extended the inca empire to the south, into what is now argentina and chile.  

in 1493 ce, huayna capac became the eleventh ruler of the inca empire.  

huayna, therefore, wanted to gain his own lands and launched campaigns against tribes to the east and north of the empire.  

the inca empire reached its peak under the rule of huayna capac.

during this time the empire covered a vast territory including parts of present day colombia, peru, argentina, chile, bolivia, and ecuador.

during his reign, huayna heard about bearded men with pale skin that resembled the incan1 god viracocha and took this news as a bad omen.

huayna took this as another bad omen that predicted the destruction of the empire.

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