Question
Which of the following are equivalent expressions?
i) 5x + 25
ii) 5(x + 5)
iii) 5x
iv) 25
- i and ii
- ii and iii
- iii and i
- iii and iv
Hint:
We are given four algebraic expressions. An algebraic expression can consist of a variable and a constant. We are asked to find which of them is an equivalent expression. For equivalent expressions, we have to rearrange the expression without changing the value of the expression.
The correct answer is: i and ii
The given expressions are
5x + 25
5(x + 5)
5x
25
For the first expression, as both are unlike terms, no further operation is possible. Unlike terms means terms having different variables or a variable and constant.
The variable of the first term is x, and it’s multiplied by 5. And 25 is added to the whole value. 25, cannot be added to the coefficient of x.
For the second expression, the terms in the bracket are unlike terms. But we can use distributive property to solve it further.
Distributive property: It says that the term outside the bracket, or in other words, in the multiplication of the bracket, gets distributed equally to the terms inside the bracket.
So we can write the third expression as
5(x + 5) = (5)x + (5)5
5(x + 5) = 5x + 25
If we see it’s the same as the first expression.
Now let’s see the third expression. The term is same as the first term in the first expression, but it doesn’t have a constant 25 added to it. So the value of the expression changes. So the third expression is not equivalent to any of the expression.
The fourth term is just a constant. It is the same constant as that of the first expression, but it doesn’t have the term ‘5x’. So the fourth expression is not equivalent to any of the expressions.
Also, for third and fourth, one has a variable and the other is constant. So they are not equivalent.
Therefore, the expressions “5x + 25” and “5(x + 5)” are equivalent expressions.
So option ‘i and ii’ is the right option.
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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