Question

Which expressions are equivalent to 3x+3(x+y) ?

Answer 1

3x+3 (x+y)=3x+3x+3y (1st expression which is equivalent )
6x+3y (2nd expression which is equivalent )

Answer 2

Given that the expression is 3x+3(x+y)

TO FIND :

The equivalent expressions to the given expression

SOLUTION :

From the given expression 3x+3(x+y)

By using the Distributive property :

a(x+y)=ax+ay

3x+3(x+y)=3x+3(x)+3(y) ( here a=3 )

=3x+3x+3y

3x+3(x+y)=3(x+x+y)

Therefore option 3(x+x+y) is correct and it is equivalent to 3x+3(x+y)

From this 3x+3(x+y)=3x+3x+3y we have

By adding the like terms

=6x+3y

3x+3(x+y)=6x+3y

Therefore option 6x+3y is correct and it is equivalent to 3x+3(x+y)

Therefore the equivalent expressions to the given expressions are 3(x+x+y) and 6x+3y