Find the missing side x​

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?

Which expression is equivalent to (5x^7+7x^8) − (4x^4−2x^8)? a. 9x^8 + 5x^7−4x^4 b. 3x^8 + 7x^7 c. 12x^8 − 2x^4 d. 5x^8 + 5x^7 + 4x^4

What are the triple angle formulas? is it related to double angle identities?