## Algebra 1

a) "$a\times b=b\times a$" is an example of the commutative property of multiplication, which says that the order in which two factors appear does not change the product. These two expressions are equivalent because the product of a and b is the same regardless of whether a or b appear first in the expression. b) These two expressions are not equivalent. It appears as though the distributive property has been applied incorrectly. The expression in parentheses is a product. The distributive property can only be used if the expression in parentheses is a sum or a difference (addition or subtraction). Let a=2, b=3 and c=4. Substitute these values and simplify to see that the result is not the same for these two expressions. $2(3\times4)\overset?=(2)(3)\times(2)(4)$ $2(12)\overset?=6\times8$ $24\ne48$