%E2%8B%85(%E2%88%922.5)-equivalent-expression.jpeg "(3−8y)⋅(−2.5) Equivalent Expression")
Finding Equivalent Expressions: (3−8y)⋅(−2.5)
In mathematics, an equivalent expression is another way to write the same mathematical idea. This means that the expression will result in the same value for any given value of the variable. Let's explore how to find an equivalent expression for (3−8y)⋅(−2.5).
The Distributive Property
The key to finding an equivalent expression is the distributive property. This property states that multiplying a sum by a number is the same as multiplying each term of the sum by the number:
a(b + c) = ab + ac
Applying the Distributive Property
Let's apply the distributive property to our expression:
- Identify the terms: Our expression is (3−8y)⋅(−2.5). Here, '3' and '-8y' are the terms inside the parentheses.
- Distribute: We multiply each term inside the parentheses by -2.5:
- (3)⋅(−2.5) = -7.5
- (−8y)⋅(−2.5) = 20y
- Combine: Now we combine the two results: -7.5 + 20y
Equivalent Expression
Therefore, the equivalent expression for (3−8y)⋅(−2.5) is -7.5 + 20y.
Verification
To check our answer, let's choose a value for 'y' and substitute it into both the original expression and the equivalent expression. If we get the same answer, we have confirmed that the expressions are equivalent.
For example, let's choose y = 1.
- Original expression: (3−8(1))⋅(−2.5) = (-5)⋅(-2.5) = 12.5
- Equivalent expression: -7.5 + 20(1) = -7.5 + 20 = 12.5
Since we get the same result (12.5) for both expressions, we have confirmed that they are equivalent.