Factorization by Grouping
Factorization by Grouping
Example 1
$$\textup{Factorize } ax+ay+bx+by$$
Solution
\begin{align*}
& \,ax+ay+bx+by\\
=& \,a(x+y)+b(x+y)\\
=& \,(x+y)(a+b)\\
\end{align*}
Example 2
$$\textup{Factorize } ax+ay+2x+2y$$
Solution
\begin{align*}
& \,ax+ay+2x+2y\\
=& \,a(x+y)+2(x+y)\\
=& \,(x+y)(a+2)\\
\end{align*}
Example 3
$$\textup{Factorize } x^2+xy+xz+yz$$
Solution
\begin{align*}
& \,x^2+xy+xz+yz\\
=& \,x(x+y)+z(x+y)\\
=& \,(x+y)(x+z)\\
\end{align*}
Example 4
$$\textup{Factorize } x^2+xy+3x+3y$$
Solution
\begin{align*}
& \,x^2+xy+3x+3y\\
=& \,x(x+y)+3(x+y)\\
=& \,(x+y)(x+3)\\
\end{align*}
Example 5
$$\textup{Factorize } 2x^2+4xy+3x+6y$$
Solution
\begin{align*}
& \,2x^2+4xy+3x+6y\\
=& \,2x(x+2y)+3(x+2y)\\
=& \,(x+2y)(2x+3)\\
\end{align*}
Example 6
$$\textup{Factorize } x^2a+x^2b+4a+4b$$
Solution
\begin{align*}
& \,x^2a+x^2b+4a+4b\\
=& \,x^2(a+b)+4(a+b)\\
=& \,(a+b)(x^2+4)\\
\end{align*}