Question

AC method, Factoring step by step I don't know how to do .

Answer 1

(5a+4c)(2a-b)

Step-by-step explanation:

Given the expression:

`10a^2-5ab+8ac-4bc`

First, group the expression into two:

`=(10a^2-5ab)+(8ac-4bc)`

• In the first group, 5a is a common factor.

,

• In the second group, 4c is a common factor.

Factor these out by dividing each term by the GCF of each group.

`\begin{gathered} =5a((10a^2)/(5a)-(5ab)/(5a))+4c((8ac)/(4c)-(4bc)/(4c)) \\ \\ =5a(2a-b)+4c(2a-b) \end{gathered}`

Since the terms inside the brackets are the same, combine:

`=(5a+4c)(2a-b)`

CHECK

To check if your result is correct in cases like these, expand as follows:

`\begin{gathered} (5a+4c)(2a-b)=5a(2a-b)+4c(2a-b) \\ =10a^2-5ab+8ac-4bc \end{gathered}`

Our result is the same as the original question, hence, the work is correct.