Simplify (3a4 – 2a2 + 5a – 10) – (2a4 + 4a2 + 5a – 2).

a. 5a4 + 4a3 + 3a2 + 10a – 12
b. a4 + 4a2 + 10a – 12
c. a4 + 2a2 + 10a – 12
d. a4 – 6a2 – 8

What is the distance between the points 4,10 and -3,-14 on the coordinate plane

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1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?