Question

3. Which of the following correctly shows the first step when factoring 3ab +3ac-4db-4dc by grouping?

O 3a(b+c)+4d(b − c)
O a(3b+3c)-d(4b+ 4c)
O 3a(b+c)+4d(b + c)
O 3a(b+c)-4d(b+c)

Answer 1

The correct first step in factoring the expression 3ab + 3ac - 4db - 4dc by grouping is to factor out the common factors from each group, resulting in 3a(b + c) - 4d(b + c).

Step-by-step explanation:

The student asked which of the following correctly shows the first step when factoring 3ab +3ac-4db-4dc by grouping.

To factor by grouping, we want to group terms that have a common factor and then factor out the common factor from each group.

Looking at the given expression, we can group the first two terms together and the last two terms together because they each share a common factor. This gives us:

• 3ab + 3ac: Both terms have a common factor of 3a.
• -4db - 4dc: Both terms have a common factor of -4d. Notice the negative sign is carried along with the common factor.

Factoring out the common factors, we get:

• 3a(b + c)
• -4d(b + c)

The correct answer is then 3a(b + c) - 4d(b + c).