Property 2
Grouping
If there isn't any common factors among all terms · they are grouped and then the common factor is performed within parenthesis.
\(ax+ay+bx+by=a\cdot\left(x+y\right)+b\cdot\left(x+y\right)\)
\(=\left(x+y\right)\cdot\left(a+b\right)\)
Factorize the following expressions to make it simple form.
1.
\(\samefrac{x^3+x^2-x-1}{x^2-1}=?\)
2.
\(\samefrac{ax+bx+ay+by}{a+b}=?\)
3.
\(\samefrac{x^2-xy+2x-2y}{x+2}=?\)
4.
\(\samefrac{x^2-3x-x+3}{x-1}=?\)
5.
\(\samefrac{a^3+2a^2-a-2}{2a^2-2}=?\)
6.
\(\samefrac{ax+ay-bx-by}{2x+2y}=?\)
7.
\(\samefrac{ax-ay+bx-by-cx+cy}{x-y}\)
8.
\(\samefrac{\left(x-y\right)^2-2\left(y-x\right)^2}{\left(y-x\right)^2}=?\)
9.
\(\samefrac{\left(x-y\right)^2-2\left(y-x\right)}{x-y+2}=?\)
10.
\(\samefrac{a\left(x-y\right)+b\left(y-x\right)}{x-y}=?\)
11.
\(\samefrac{a\left(y-x\right)+a\left(x-y\right)+b\left(y-x\right)}{y-x}=?\)
12.
\(\samefrac{\left(x-y\right)^2+\left(y-x\right)^3}{\left(y-x\right)^2}=?\)
13.
\(\samefrac{3x-3y}{x-y}+\samefrac{2y+2x}{x+y}+\samefrac{\left(x-y\right)^4}{\left(y-x\right)^4}=?\)
14.
\(\samefrac{a^2x+ay-b^2x+by}{ax-bx+y}=?\)
15.
\(\samefrac{x^3-x^2y+3x^2y-3xy^2}{x^3-x^2y-3x^2y+3xy^2}=?\)