classify each statement as sometimes, always, or never true. give examples or properties to support your answer a+ (bc) =( a+b) .(a+c)
What is your answer?
sometimes
Sometimes never maybe yes.
To determine whether the statement "a + (bc) = (a + b) ⋅ (a + c)" is sometimes, always, or never true, we can use an example and properties of algebra to support our answer.
Let's consider the statement for different values of variables a, b, and c.
Example 1:
Let a = 1, b = 2, and c = 3.
Substituting these values into the equation:
1 + (2⋅3) = (1 + 2) ⋅ (1 + 3)
1 + 6 = 3 ⋅ 4
7 = 12
Since 7 is not equal to 12, the statement is NOT always true.
Example 2:
Let a = 0, b = 2, and c = 3.
Substituting these values into the equation:
0 + (2⋅3) = (0 + 2) ⋅ (0 + 3)
0 + 6 = 2 ⋅ 3
6 = 6
Since 6 is equal to 6, the statement is sometimes true.
By observing these examples, we can conclude that the statement "a + (bc) = (a + b) ⋅ (a + c)" is sometimes true, but not always.