Question

How do you factor by grouping $ac-bc+ad-bd$?

Answer 1

Hint: To do this, you need to find the terms which are common. As you can see in the terms ac and bc, the term c is common and in the term ad and bd , the term d is common. Now you can see that after you take c and d as common from the terms, you get a – b as the common term. So now you are left with the term c + d. Now you get the final answer.

Complete step by step solution:
Here is the complete step by step solution.
The first step we need to do is to find the terms which are common. As you can see in the terms ac and bc, the term c is common and in the term ad and bd , the term d is common. Therefore, after taking them as common, we get
$\Rightarrow ac-bc+ad-bd$
$\Rightarrow c\left( a-b\right) + d\left( a-b\right) $
Now we can see that after we take c and d as common from the terms, we get a – b as the common term. Therefore, we take it out and we are left with the term c+ d . Therefore, we get
$\Rightarrow \left( a-b\right) \left( c+d\right) $
Therefore, we get the final answer of the question, how do you factor by grouping as $ ac-bc+ad-bd$ as $ \left( a-b\right) \left( c+d\right)$.

Note: Whenever you do these kinds of questions, the first thing you need to do is to find the terms which are common. Then you can solve the question easily. You need to be careful while taking out the common terms. You can verify the answer by multiplying all the terms using the distribution law .