Could you explain how to factor completely
-a^3n+1 + 2b^2n+b - ab - (2a^3n*b^2n)
What is 7/12 as a decimal and a percent???
To factor completely, we'll need to look for common terms that can be factored out and then use appropriate factoring techniques. Let's break down the expression you provided:
-a^3n+1 + 2b^2n + b - ab - (2a^3n*b^2n)
Step 1: Group common terms
Group the terms together based on the common factors they share. In this case, we can group the terms as follows:
((-a^3n+1 - ab) + (2b^2n + b)) - (2a^3n*b^2n)
Step 2: Factor out the common factors from each group
Now we'll factor out the common factors from each group of terms. Let's start with the first group:
Common factor: -a
-a^3n+1 - ab
Factored expression:
-a(an+1) - ab
Next, let's factor out the common factor from the second group:
Common factor: b
2b^2n + b
Factored expression:
b(2bn + 1)
Step 3: Simplify the remaining expression
Now we'll simplify the remaining expression:
(2a^3n*b^2n)
Step 4: Combine the factored groups
Now that we have factored out the common factors from each group, we can combine them back together:
(-a(an+1) - ab) + (b(2bn + 1)) - (2a^3n*b^2n)
Which can be written as:
-a(an + 1) - ab + b(2bn + 1) - 2a^3n*b^2n
Thus, the completely factored expression is:
-a(an + 1) + b(2bn + 1) - ab - 2a^3n*b^2n