Question

1. Which of the following pairs contain like terms? a. \( 2 x \) and \( 5 x \) b. \( 5 a^{2} \) and \( 6 a^{2} \) c. \( x^{2} \) and \( 2 x^{3} \) d. \( 3 x^{2} \) and \( 2 y^{2} \) e. 3 and \( y \) f. \( x^{5} \) and \( 6 x^{5} \) 2. For any three real numbers \( a, b \) and \( c \), determine whether each of the following statements is true or false. Give reason for your answer. a. \( a+b=b+a \) b. \( a-b=b-a \) c. \( (a+b)+c=a+(b+c) \) d. \( (a b) c=a(b c) \) e. \( a(b+c)=a b+a c \) f. \( a-(b+c)=a-b+c \) g. \( a-(b-c)=a-b+c \) h. \( (a-b)+c=a+(-b+c) \)

          1. Which of the following pairs contain like terms?
a. \( 2 x \) and \( 5 x \)
b. \( 5 a^{2} \) and \( 6 a^{2} \)
c. \( x^{2} \) and \( 2 x^{3} \)
d. \( 3 x^{2} \) and \( 2 y^{2} \)
e. 3 and \( y \)
f. \( x^{5} \) and \( 6 x^{5} \)
2. For any three real numbers \( a, b \) and \( c \), determine whether each of the following statements is true or false. Give reason for your answer.
a. \( a+b=b+a \)
b. \( a-b=b-a \)
c. \( (a+b)+c=a+(b+c) \)
d. \( (a b) c=a(b c) \)
e. \( a(b+c)=a b+a c \)
f. \( a-(b+c)=a-b+c \)
g. \( a-(b-c)=a-b+c \)
h. \( (a-b)+c=a+(-b+c) \)

1. Which of the following pairs contain like terms?
a. 2 x and 5 x
b. 5 a^2 and 6 a^2
c. x^2 and 2 x^3
d. 3 x^2 and 2 y^2
e. 3 and y
f. x^5 and 6 x^5
2. For any three real numbers a, b and c, determine whether each of the following statements is true or false. Give reason for your answer.
a. a+b=b+a
b. a-b=b-a
c. (a+b)+c=a+(b+c)
d. (a b) c=a(b c)
e. a(b+c)=a b+a c
f. a-(b+c)=a-b+c
g. a-(b-c)=a-b+c
h. (a-b)+c=a+(-b+c)

Added by Todd F.

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