Equivalent Expressions
Two or more expressions are equivalent if they have the same value even if they look different.
We have the expression 2c + 6d. We can transform it to make it look different but without changing its value.
For example, we can divide and multiply it by 2:
Dividing each term by 2:
This expression is equivalent to the original because we made two opposite operations on it, leaving it unchanged, but with a different look.
Now we'll find another expression by adding and subtracting 4c:
2c + 6d + 4c - 4c
This expression is equivalent to the original because we did two opposite operations. But let's go further on this one. Adding 2c+4c=6c:
6c + 6d - 4c
Factoring 6 from the two first terms:
6 (c + d) - 4c
This new expression looks quite different from the original, but they are equivalent.