Question
Write the equivalent expressions for the following:
20y + 30x
- 10(2y + 3x)
- 10(2y)
- 10x
- 10y
Hint:
We are given an algebraic expression. An algebraic expression consists of variables and constants. A variable is a quantity that doesn’t have any fixed value. A constant is a quantity with a fixed value. For this question, we have to perform the operation using the properties and find the equivalent expression.
The correct answer is: 10(2y + 3x)
The given expression is 20y + 30x.
The above expression has two variables: ‘x’ and ‘y’.
The terms are unlike terms. Unlike terms are the terms with different variables or a variable and constant.
As the terms are unlike terms, no further operation is possible.
But we can use the distributive property. Distributive property: It states the quantity outside the bracket is distributed equally to the terms inside the bracket. The reverse is also true. We can take a common multiple outside of the bracket.
We can see that both 20 and 30 are even numbers and have zero as end digit. So it is a multiple of 10
So the equation becomes
20y + 30x = (10)2y + (10)3x
We can take 10 common out of both the terms.
20y + 30x = 10(2y + 3x)
Therefore, the equivalent expression is 10(2y + 3x).
For such questions, we should know the basic properties to solve am algebraic expression. We have to be careful about different variables.
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