Question

4. Divide : (a) (a³-a²b-ab + b²) by (a - b) ​

Answer 1

Answer: =(a)(a²-b)

Explanation:

(a) (a³-a²b-ab + b²) by (a - b)

`((a) (a^(3) -a^(2) b-ab + b^(2) ))/((a - b))` >Factor by grouping, group the first 2 terms

and last

`=((a)[ (a^(3) -a^(2) b)(-ab + b^(2) )])/((a - b))` >Take out GCF

`=((a)[a^(2) (a - b)-b(a - b )])/((a - b))` >Take out GCF (a-b) on top

`=((a)[ (a - b)(a^(2) -b )])/((a - b))` >cross off common (a-b)

=(a)(a²-b)

Answer 2

Explanation:

To divide the expression (a³ - a²b - ab + b²) by (a - b), we can use polynomial long division. Here are the steps:

```

a^2 + ab + b^2

-----------------------

a - b | a^3 - a^2b - ab + b^2

- (a^3 - ab^2)

-----------------------

ab - ab^2 + b^2

- (ab - b^2)

-----------------------

b^2

```

The quotient is a² + ab + b², and the remainder is b².

Therefore, the result of dividing (a³ - a²b - ab + b²) by (a - b) is a² + ab + b² with a remainder of b².