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*}