Question
Are 3(3x – 5) and 9x – 15 equivalent expressions?
- Yes
- No
- Either yes or no
- None of the above
Hint:
We are given two algebraic expressions. An algebraic expression can consist of a variable and a constant. We are asked to find if the equivalent expressions. For equivalent expressions, we have to rearrange the expression without changing the value of the expression.
The correct answer is: Yes
The given expressions are 3(3x – 5 ) and 9x – 15.
Let’s see first expression.
The terms inside the bracket are unlike terms. Unlike terms have different variable. So, no further operation is possible for the terms inside the bracket.
For the second both are unlike terms. So, no further operation is possible.
We can solve the first expression further if we use the distributive property.
Distributive property says that, the term outside the bracket or in other words, in multiplication with bracket, can be disturbed equally inside the bracket.
So the expression becomes
3(3x – 5) = (3)3x – (3)5
3(3x – 5) = 9x – 15
No further operation is possible.
If we compare this to the second expression, we can see that both terms have same terms and same operation. So both the expressions are equivalent.
The given expressions are equivalent.
So the right option is the option that says ‘Yes’.
For such questions, we should be familiar with the different properties required to perform algebraic expression. At the same time we should know the basic rules of operations of algebraic expression.
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