The required **expression **that has an even **integer **value for all integers a and c is F. 8a + 2ac.
What is simplification?
**Simplification **involves applying rules of **arithmetic **and algebra to remove unnecessary terms, factors , or **operations **from an expression.
Here, We can determine which expressions have an even integer value for all integers a and c by looking at their factors.
An integer is even if and only if it is divisible by 2. Therefore, an expression will have an even integer value for all integers a and c if and only if it contains a factor of 2.
Let's look at each of the given expressions:
F. 8a + 2ac = 2(4a + ac)
This expression has a factor of 2, so it has an even integer value for all integers a and c.
G. 3a + 3c = 3(a + c)
This expression does not have a factor of 2, so it does not have an even integer value for all integers a and c.
H. 2a + c
This expression does not have a factor of 2, so it does not have an even integer value for all integers a and c.
J. a + 2c
This expression does not have a factor of 2, so it does not have an even integer value for all integers a and c.
K. ac + a²
This expression does not have a factor of 2, so it does not have an even integer value for all integers a and c.
Therefore, the **expression **that has an even **integer **value for all integers a and c is F. 8a + 2ac.
Learn more about **simplification **here:
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The expression that has an even integer value for all integers a and c is F. 8 a + 2 a c since it contains a factor of 2. Other options may yield odd values depending on the integers chosen. Thus, F is the only expression guaranteed to be even for all integers.
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