#14 x ^{2} y ^{3} - 21 xy ^{2} + 7 x ^{3} y ^{2} = 7 xy ^{2}(2 xy - 3 + x ^{2}) = 7 xy ^{2}( x ^{2} + 2 xy - 3) #

Börja med att förenkla genom att multiplicera ihop parenteserna.

#2 x ( x ^{3} - 4)( x + 3) - (2 x ^{5} - 24 x ) = #

#= 2 x ( x ^{4} + 3 x ^{3} - 4 x - 12) - 2 x ^{5} + 24 x = #

#= 2 x ^{5} + 6 x ^{4} - 8 x ^{2} - 24 x - 2 x ^{5} + 24 x = #

#= 6 x ^{4} - 8 x ^{2} #

Faktorn #2 x # får bara multipliceras in i # en # parentes. Om #2 x # multipliceras in i båda parenteserna så motsvarar det multiplikation med faktorn #4 x ^{2}. #

#\frac{{12{x^3}{y^2} - 16{x^2}{y^3}}}{{4{x^3}{y^2} - 8{x^2}{y^2}}} = \frac{{4{x^2}{y^2}(3x - 4y)}}{{4{x^2}{y^2}(x - 2)}} = \frac{{(3x - 4y)}}{{(x - 2)}}#

#\frac{2}{x^2-2x} - \frac{2}{x^2-4} =#

#= \frac{{2\color{royalblue}{({x^2} - 4)}}}{{({x^2} - 2x)\color{royalblue}{({x^2} - 4)}}} - \frac{{2\color{royalblue}{({x^2} - 2x)}}}{{\color{royalblue}{({x^2} - 2x)}({x^2} - 4)}} = #

#= \frac{{2{x^2} - 8 - (2{x^2} - 4x)}}{{({x^2} - 2x)({x^2} - 4)}} = \frac{{\color{darkorchid}{2{x^2}} - 8 - \color{darkorchid}{2{x^2}} + 4x}}{{({x^2} - 2x)({x^2} - 4)}} =#

#= \frac{{4x - 8}}{{({x^2} - 2x)({x^2} - 4)}} = \frac{{4\color{darkorchid}{(x - 2)}}}{{x\color{darkorchid}{(x - 2)}({x^2} - 4)}} =#

#= \frac{4}{{x({x^2} - 4)}} = \frac{4}{{{x^3} - 4x}}#