Question

a³ - a² + ab² - a²b² factorise​

Answer 1

Answer:

$a(a-1)(a-b^{2} )$

Step-by-step explanation:

Given : $a^{3} -a^{2} +ab^{2} -a^{2} b^{2}$

To find : Factors of the given polynomial.

Solution :  

• The given polynomial is,

       $a^{3} -a^{2} +ab^{2} -a^{2} b^{2}$

• taking out common factors from the groups of two terms, we get

       $a^{3} -a^{2} +ab^{2} -a^{2} b^{2} = a^{2} (a-1)-ab^{2} (-1+a)$

• Rearranging the terms, we get

                           $= a^{2} (a-1)-ab^{2} (a-1)$

                           $= (a-1)(a^{2}-ab^{2})$

• Now, taking out common terms from second bracket, we get

                          $= a(a-1)(a-b^{2} )$                      

Answer 2

Given equation is,

$a^{3} -a^{2} +ab^{2} -a^{2} b^{2}$

Now we have to factorize this equation.

Take $a^{2}$ common from first two terms and take $-ab^{2}$ common from last two terms.

We get,

$a^{2} (a-1)-ab^{2} (-1+a)$

$a^{2} (a-1)-ab^{2} (a-1)$

Again take $(a-1)$ common from above two terms.

We get,

$(a-1)(a^{2} -ab^{2} )$

Again take $(a)$ common from above second term

$(a-1)(a)(a-b^{2} )$

Therefore the final answer after factorization is $(a-1)(a)(a-b^{2} )$