Question

Factorise: $ {a^2}b + a{b^2} - abc - {b^2}c + axy + bxy $

Answer 1

Hint: To find the factorization of any given expression means we have to reduce that expression to simplest terms which are called the factor of the expression. To find the factorise we have to take out the common values or expressions from the given expression.

Complete step-by-step answer:
The given expression is $ {a^2}b + a{b^2} - abc - {b^2}c + axy + bxy $ .
The first two terms of the expression have a as well as b so we can take \[ab\] as common from first two term then we get,
 $ ab\left( {a + b} \right) - abc - {b^2}c + axy + bxy $
In next two terms b and c is common so we take out $ bc $ as common from them then we get,
$\Rightarrow ab\left( {a + b} \right) - bc\left( {a + b} \right) + axy + bxy $
As we take the negative sign out of the common hence the sign under the bracket gets converted. Now again taking $ xy $ as common from last two terms then we get,
$\Rightarrow ab\left( {a + b} \right) - bc\left( {a + b} \right) + xy\left( {a + b} \right) $
If you have noticed then you will find after taking out common we get equal expression under the brackets. So we will take it common from whole expression then,
$\Rightarrow \left( {a + b} \right)\left( {ab - bc + xy} \right) $
Now we will repeat the same steps with the remaining expression as given below:
$\Rightarrow \left( {a + b} \right)\left( {ab - bc + xy} \right) $
But as we see that there should be no possibility of common as the above expression is the factorise form of given expression.

Note: You have to take out the factor or make the expression in simple form until there is no possibility of taking out multiple forms. These simplest values are called the factor of the given expression as they can divide the expression completely. This factorization can also be performed by using identities, which will find the factor quickly.