Question

write 2 equivalent expressions for 2c + 6d

Answer 1

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:

$2\cdot\frac{2c+6d}{2}$

Dividing each term by 2:

$2\cdot(c+3)$

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.