A method of factoring an expression (a polynomial) by grouping the terms to take out the common factor from them is called the factorization (or factorisation) by grouping.
In mathematics, it is essential to simplify the expressions by factorization in some cases and it is only possible to factorize some polynomials by grouping. So, let’s learn how to factorise the expressions by grouping.
An expression can be factored by grouping in three simple following steps.
Remember, the common factors are taken out from the terms according to the distributive property.
The polynomial contains four terms and observe them for common factors. The first and fourth terms contains a common factor $3$. Similarly, the second and third terms have $xy$ as a common factor. So, write all the terms in groups first.
$= \,\,\,$ $x^2y+3xy+3x+9$
$= \,\,\,$ $(x^2y+3xy)+(3x+9)$
Now, factorise each group by taking common factors out from the groups.
$= \,\,\,$ $xy(x+3)+3(x+3)$
The given algebraic expression now has two terms but they have $x+3$ as a common factor. So, take the common factor out from the groups.
$= \,\,\,$ $(x+3)(xy+3)$
Therefore, the algebraic expression $9+3xy+x^2y+3x$ is factored as $(x+3)(xy+3)$ by grouping in mathematics.
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