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
a. F
b. T
c. T
d. T
To determine whether each statement is true or false, we need to analyze the given expressions and statements.
a. 2x is a factor of the expression (2x + y).
For 2x to be a factor of (2x + y), we need to check if 2x divides evenly into (2x + y) without any remainder. To do this, we can simplify the expression (2x + y) by factoring out common terms:
(2x + y) = x(2) + y = 2x + y
Since (2x + y) is the exact same expression as the original expression, we can conclude that 2x is not a factor of (2x + y).
Therefore, the statement "2x is a factor of the expression (2x + y)" is false.
b. (2x + y) is a factor of the expression 3(2x + y).
Similar to the previous statement, we can simplify the expression 3(2x + y) by distributing the 3 to each term inside the parentheses:
3(2x + y) = 3(2x) + 3(y) = 6x + 3y
In this case, (2x + y) is different from the original expression 3(2x + y).
Therefore, the statement "(2x + y) is a factor of the expression 3(2x + y)" is false.
c. (2x + y) is a sum of two terms.
In mathematics, terms are separated by addition or subtraction. In the expression (2x + y), there are no addition or subtraction signs between 2x and y. Therefore, (2x + y) is not a sum of two terms, as it is composed of two terms directly combined with a plus sign.
Therefore, the statement "(2x + y) is a sum of two terms" is false.
d. 3(2x + y) is a product of two terms.
In the expression 3(2x + y), (2x + y) is being multiplied by 3. Since multiplication involves two factors, in this case, 3 and (2x + y), we can say that 3(2x + y) is indeed a product of two terms.
Therefore, the statement "3(2x + y) is a product of two terms" is true.
Summary:
a. False
b. False
c. False
d. True