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*}