Why did anti-slavery advocates from the North core if new territories entered
the Union as free states or slave states?

If new states entered the union as a slave state it would result in an unequal number of slave states as compared to non slave states. Slave states would out number non slave states allowing for more representatibves in congress and the senate resulting in an unequal distribution of power. They feard that if we increased the number of slave states that the slave states would gain the upper hand.

Explanation:

answer; (d) all of the above; 100%

answer; ethnocentrism;