take into consideration the expressions 3 2 + 1 and also 5 × 2 . Both space equal come 10 . That is, castle are tantamount expressions.

now let us take into consideration some expressions that encompass variables, say 5 x + 2 .

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

We can re-group the right side that the equation to 2 x + 3 x + 1 + 1 or x + 4 x + 2 or some other combination. All these expressions have the same value, anytime the exact same value is substituted because that x . That is, lock are indistinguishable expressions.

2 expressions are claimed to be indistinguishable if they have the exact same value irrespective of the worth of the variable(s) in them.

example 1: space the two expressions 2 y + 5 y − 5 + 8 and also 7 y + 3 equivalent? define your answer.

integrate the prefer terms that the very first expression.

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

Also, − 5 and also 8 can be linked to obtain 3 .

Thus, 2 y + 5 y − 5 + 8 = 7 y + 3 .

Therefore, the 2 expressions are equivalent.

example 2: are the two expressions 6 ( 2 a + b ) and also 12 a + 6 b equivalent? define your answer.

usage the Distributive regulation to increase the an initial expression.

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

Therefore, the two expressions room equivalent.

example 3: inspect whether the 2 expressions 2 x + 3 y and 2 y + 3 x equivalent.

The first expression is the amount of 2 x "s and 3 y "s conversely, the 2nd one is the amount of 3 x "s and also 2 y "s.

Let us evaluate the expressions for some worths of x and y . Take x = 0 and also y = 1 .

2 ( 0 ) + 3 ( 1 ) = 0 + 3 = 3 2 ( 1 ) + 3 ( 0 ) = 2 + 0 = 2

So, there is at least one pair of values of the variables for which the two expressions are not the same.

Therefore, the 2 expressions room no equivalent.

example 4: examine whether the 2 expressions 3   ×   m   ×   m m and m + m + m equivalent.

take into consideration the an initial expression for any kind of non-zero values of the variable.

publication the typical terms.

3   ×   m   ×   m m = 3 m

integrate the prefer terms the the second expression.

m + m + m = 3 m

So, 3   ×   m   ×   m m = m + m + m once m ≠ 0 .

when m = 0 , the expression 3   ×   m   ×   m m is no defined.

the is, the expressions room equivalent except when m = 0 . They are not tantamount in general.

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