Question

Factorise : (1) $ {x^3} - 144x $

Answer 1

Hint: Factorizing is the reverse of expanding brackets so it is for example, putting $ 2{x^2} + x - 3 $ into the brackets from $ \left( {2x + 3} \right)\left( {x - 1} \right) $

Complete step-by-step answer:
Given, $ {x^3} - 144x $
Factor $ x $ out of $ {x^3} - 144x $
Factor $ x $ out of $ {x^3} $
 $ x.{x^2} - 144x $
Factor $ x $ out of $ - 144x $
 $ x $ . $ {x^2} + - 144.x $
Factor $ x $ is out of $ x $ . $ {x^2} + x. - 144 $
 $ x({x^2} - 144) $
Rewrite $ 144 $ as $ {12^2} $
 $ x\left( {{x^2} - {{12}^2}} \right) $
Additional information:
Since both terms are perfect squares. Factor using the difference of squares formula.
\[x\left( {\left( {x + 12} \right)\left( {x - 12} \right)} \right)\]
Remove unnecessary parenthesis
 $ x\left( {x + 12} \right)\left( {x - 12} \right) $
So the factorized of $ {x^3} - 144x $ is $ x\left( {x + 12} \right)\left( {x - 12} \right) $

Note: Some simple method for factorization
1) Factoring out the GCF.
2) The sum product pattern.
3) The grouping method.
4) The perfect square trinomial pattern.
5) The difference of square pattern.