Question

What are equivalent expressions?

Answer 1

Answer:

Consider the expressions 32+1 and 5×2 . Both are equal to 10 . That is, they are equivalent expressions.

Now let us consider some expressions that include variables, say 5x+2 .

The expression can be rewritten as 5x+2=x+x+x+x+x+1+1 .

We can re-group the right side of the equation to 2x+3x+1+1 or x+4x+2 or some other combination. All these expressions have the same value, whenever the same value is substituted for x . That is, they are equivalent expressions.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Example 1:

Are the two expressions 2y+5y−5+8 and 7y+3 equivalent? Explain your answer.

Combine the like terms of the first expression.

Here, the terms 2y and 5y are like terms. So, add their coefficients. 2y+5y=7y .

Also, −5 and 8 can be combined to get 3 .

Thus, 2y+5y−5+8=7y+3 .

Therefore, the two expressions are equivalent.

Example 2:

Are the two expressions 6(2a+b) and 12a+6b equivalent? Explain your answer.

Use the Distributive Law to expand the first expression.

6(2a+b)=6×2a+6×b                     =12a+6b

Therefore, the two expressions are equivalent.

Answer 2

Answer:

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

Hope this helps!