Question
Are 9x + 81y and 3(4x + 27y) 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: No
The given expressions are 9x + 81y and 3(4x + 27y)
Let’s see the first expression.
The first expression has both unlike terms. Unlike terms do not have same variable. We can see there are two terms in the above expression with different variables. So, no further operation is possible.
The terms inside the bracket are unlike terms. So, no further operation is possible.
We can solve the second 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(4x + 27y) = (3)4x + (3)27y
3(4x + 27y) = 12x + 81y
When we compare the first and second expressions, we can see that their second terms are identical, and they share the same operation. But their first terms are different, because both of the first terms have different coefficients. The coefficient for the first expression is 9 and for the second is 12. So, both expressions have different values. So the first and second expressions are not equivalent.
So the right option is the option that says ‘No'
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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