Assume a and b are nonzero rational numbers and c is an irrational number. For each of the following expressions, determine whether the result is irrational, rational, or both. Justify your answers. Part A: a(b + c) (1 point) Part B: (1 point) Part C: ab + ab2 (2 points)

Answer:A.Irrational number C.Rational numberStep-by-step explanation:We are given that a and b are non zero rational number and c is an irrational number .A.We have to find a(b+c) is rational, irrational or both.a=Rational number b=Rational number c=Irrational numberWe know that sum of a rational number and an irrational number=Irrational number.Therefore, b+c=Irrational number When an irrational number multiplied by a rational number then it is an irrational number.Suppose , a=1 and b=5c=[tex]\sqrt3[/tex][tex]b+c=2+\sqrt3[/tex][tex]a\cdot(b+c)=1\cdot (2+\sqrt3)=2+\sqrt3[/tex]Hence, a(b+c) is an irrational number.C.We [tex]ab+ab^2[/tex][tex]b^2=b\cdot b[/tex]=Rational numberab=Rational number.[tex]ab^2=[/tex]Rational numberProduct of  two rational number is also rational number .Sum of two rational numbers is also rational number.Hence, [tex]ab+ab^2[/tex] is a rational number.