Here is a example: of how to do it.
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.
Ex 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.
Ex 3:
Check whether the two expressions 2x+3y and 2y+3x equivalent.
The first expression is the sum of 2x 's and 3y 's whereas the second one is the sum of 3x 's and 2y 's.
Let us evaluate the expressions for some values of x and y . Take x=0 and y=1.
2(0)+3(1)=0+3=32(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 two expressions are not equivalent.
Ex 4:
Check whether the two expressions 3 × m × mm and m+m+m equivalent.
Consider the first expression for any non-zero values of the variable.
Cancel the common terms.
3 × m × mm=3m
Combine the like terms of the second expression.
m+m+m=3m
So, 3 × m × mm=m+m+m when m≠0 .
When m=0 , the expression 3 × m × mm is not defined.
That is, the expressions are equivalent except when m=0 . They are not equivalent in general.
Heres the awnser:
the awnser is B.
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