Answer:
(5a+4c)(2a-b)
Explanation:
Given the expression:
[tex]10a^2-5ab+8ac-4bc[/tex]
First, group the expression into two:
[tex]=(10a^2-5ab)+(8ac-4bc)[/tex]
• 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.
[tex]\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}[/tex]
Since the terms inside the brackets are the same, combine:
[tex]=(5a+4c)(2a-b)[/tex]
CHECK
To check if your result is correct in cases like these, expand as follows:
[tex]\begin{gathered} (5a+4c)(2a-b)=5a(2a-b)+4c(2a-b) \\ =10a^2-5ab+8ac-4bc \end{gathered}[/tex]
Our result is the same as the original question, hence, the work is correct.
