determine wether the following exspressions are equivalent
94a+28 and 108a-14(a-2)
To determine whether the expressions 94a + 28 and 108a - 14(a - 2) are equivalent, we need to simplify the second expression and check if it equals the first expression.
Expanding the second expression:
108a - 14(a - 2) = 108a - 14a + 28
= 94a + 28
Thus, the two expressions are equivalent.
can you explain to me why they are equivalent
Sure! Let's break it down step by step:
The initial expression is 94a + 28.
To simplify the second expression, we need to distribute the -14 to both terms inside the parentheses:
108a - 14(a - 2)
Distributing the -14:
= 108a - 14a + 28
Combining like terms:
= 94a + 28
When we simplify the second expression, we end up with the same expression as the first one, 94a + 28. This indicates that the two expressions are equivalent because they have the same simplified form.
To determine whether the expressions 94a + 28 and 108a - 14(a - 2) are equivalent, we need to simplify both expressions and compare the results.
Let's start with the first expression: 94a + 28
There is no simplification we can do for this expression since 28 is already a constant. So, we leave it as is.
Now let's simplify the second expression: 108a - 14(a - 2)
To simplify this expression, we need to distribute the -14 into the parentheses. This means multiplying -14 by each term inside the parentheses, which gives us:
108a - 14a + 28
Now, we can combine like terms. The like terms in this expression are 108a and -14a. Adding or subtracting them together gives us:
94a + 28
Interestingly, we arrived at the same expression as the first one. This means that the two expressions, 94a + 28 and 108a - 14(a - 2), are indeed equivalent.
So, the answer is yes, the expressions are equivalent.