Question

(a4-a3+a2-a+1)(a3-2)

Answer 1

Pulling out like terms :

 2.1     Pull out like factors :

   a4 + a3 - a2 - a  = 

  a • (a3 + a2 - a - 1) 

Checking for a perfect cube :

 2.2    a3 + a2 - a - 1  is not a perfect cube 

Trying to factor by pulling out :

 2.3      Factoring:  a3 + a2 - a - 1 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -a - 1 
Group 2:  a3 + a2 

Pull out from each group separately :

Group 1:   (a + 1) • (-1)
Group 2:   (a + 1) • (a2)
               -------------------
Add up the two groups :
               (a + 1)  •  (a2 - 1) 
Which is the desired factorization

Trying to factor as a Difference of Squares :

 2.4      Factoring:  a2 - 1 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1
Check :  a2  is the square of  a1 

Factorization is :       (a + 1)  •  (a - 1) 

Multiplying Exponential Expressions :

 2.5    Multiply  (a + 1)  by  (a + 1) 

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (a+1)  and the exponents are :
          1 , as  (a+1)  is the same number as  (a+1)1 
 and   1 , as  (a+1)  is the same number as  (a+1)1 
The product is therefore,  (a+1)(1+1) = (a+1)2 

Final result :

a • (a + 1)2 • (a - 1)

Hope this will help you a lot..
pls mark me as brainliest