Question

Factorize b²-ab(1-a)-a³
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Answer 1

To factorize :   $b^{2} - ab (1 - a ) - a^{3}$

Solution :

• To factorize  we write given expression in proper form :

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

• Now, by taking $b$ common from first two terms and $a$  from last two terms we get,

          ⇒     $b( b - a ) + a^{2} ( b - a )$

• Again taking $( b - a )$  as common we get,

          ⇒      $( b - a ) ( b + a^{2})$

        Hence , factors of $b^{2} - ab (1 - a ) - a^{3}$  are    $( b - a ) ( b + a^{2})$

Answer 2

Given equation is,

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

Now we have to factorize the given equation

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

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

Now we have to take $b$ common from first two terms and $a^{2}$ common from last two terms.

We get the equation as,

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

Again take $(b-a)$ common from both the terms.

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

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