Question

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

Answer 1

Answer:

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

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.

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

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.