Question

Which expressions are equivalent to the expression 4a – 6b + 3c?

a + 3(a − 2b + 3c)
4a + 3(2b + c)
2(2a − 3b + c) + c
2(2a − 3b) + 3c

Answer 1

To determine which expressions are equivalent to 4a - 6b + 3c, distribute the coefficients and simplify each expression.

Step-by-step explanation:

To determine which expressions are equivalent to 4a - 6b + 3c, we can distribute the coefficients and simplify the expressions. Let's go through each option:

1. a + 3(a - 2b + 3c)
   By distributing, we get: a + 3a - 6b + 9c
   Combining like terms, we obtain: 4a - 6b + 9c
   This expression is equivalent to the original.
2. 4a + 3(2b + c)
   By distributing, we get: 4a + 6b + 3c
   This expression is not equivalent to the original.
3. 2(2a - 3b + c) + c
   By distributing, we get: 4a - 6b + 2c + c
   Combining like terms, we obtain: 4a - 6b + 3c
   This expression is equivalent to the original.
4. 2(2a - 3b) + 3c
   By distributing, we get: 4a - 6b + 3c
   This expression is equivalent to the original.

So, the expressions that are equivalent to 4a - 6b + 3c are: a + 3(a - 2b + 3c), 2(2a - 3b + c) + c, and 2(2a - 3b) + 3c.

Answer 2

4a + 3(2b + c)

2(2a − 3b + c) + c

2(2a − 3b) + 3c

Step-by-step explanation: