Indicate whether each statement is true or false by checking the appropriate box in the table below.
a. 2x is a factor of the expression (2x + y ). True or False
b. (2x + y ) is a factor of the expression 3(2x + y ). True or False
c. (2x + y ) is a sum of two terms. True or False
d. 3(2x + y ) is a product of two terms. True or False
No one has answered this question yet.
a. false
b. true
c. true
d. true
correct
To determine whether each statement is true or false, let's analyze each one:
a. 2x is a factor of the expression (2x + y).
- This statement is true. We can see that 2x is a factor of the given expression because it can be factored as (2x + y) = 2x(1 + y/2x).
b. (2x + y) is a factor of the expression 3(2x + y).
- This statement is true. The expression 3(2x + y) can be factored as (3)(2x + y) = (2x + y)(3). Therefore, (2x + y) is a factor.
c. (2x + y) is a sum of two terms.
- This statement is false. The expression (2x + y) consists of only one term, which is the sum of 2x and y.
d. 3(2x + y) is a product of two terms.
- This statement is true. The expression 3(2x + y) can be viewed as the product of two terms, namely 3 and (2x + y).
Therefore, the final answer would be as follows:
a. True
b. True
c. False
d. True
To determine whether each statement is true or false, we need to understand the concepts related to factors, terms, and products in algebraic expressions.
a. To check whether 2x is a factor of the expression (2x + y), we need to determine if dividing (2x + y) by 2x would result in a whole number. In this case, if we divide (2x + y) by 2x, we would get (1 + y/2x). Since y/2x is not a whole number for all values of y, 2x is not a factor of (2x + y). Therefore, the statement is False.
b. To check whether (2x + y) is a factor of the expression 3(2x + y), we need to determine if dividing 3(2x + y) by (2x + y) would result in a whole number. In this case, if we divide 3(2x + y) by (2x + y), we would get 3. Since 3 is a whole number, (2x + y) is a factor of 3(2x + y). Therefore, the statement is True.
c. To determine whether (2x + y) is a sum of two terms, we need to identify if the expression consists of two distinct terms with a plus sign between them. In this case, (2x + y) does consist of two terms, 2x and y, separated by a plus sign. Therefore, the statement is True.
d. To determine whether 3(2x + y) is a product of two terms, we need to identify if the expression consists of two distinct terms with a multiplication sign between them. In this case, 3(2x + y) is the result of multiplying 3 by (2x + y), so it represents a product. Therefore, the statement is True.
Based on the explanations above, the answers to the statements are as follows:
a. False
b. True
c. True
d. True