Answer true or false to each statement. Explain why each false statement is incorrect.a 2x and − 2x are like terms. b 15a and 15 a2 are like terms.c 8p and p_5 are like terms. d 5_8 def and 5fed are like terms.e 4ab and 6a2b are like terms.
Question
Answer true or false to each statement. Explain why each false statement is incorrect.a 2x and − 2x are like terms. b 15a and 15 a2 are like terms.c 8p and p_5 are like terms. d 5_8 def and 5fed are like terms.e 4ab and 6a2b are like terms.
Solution
a) False. 2x and -2x are not like terms. Like terms are terms that have the same variables and powers. The variables are the same here (x), but the coefficients are different (2 and -2).
b) False. 15a and 15a^2 are not like terms. Like terms must have the same variables and powers. Here, the variable 'a' in 15a has a power of 1, while in 15a^2, 'a' has a power of 2.
c) False. 8p and p_5 are not like terms. Like terms must have the same variables and powers. Here, the variable in the first term is 'p', while in the second term it is 'p_5'. These are not the same.
d) False. 5_8 def and 5fed are not like terms. Like terms must have the same variables and powers. Here, the variables are 'def' and 'fed', which are not the same.
e) False. 4ab and 6a^2b are not like terms. Like terms must have the same variables and powers. Here, the variable 'a' in 4ab has a power of 1, while in 6a^2b, 'a' has a power of 2.
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