Question

factorise: a^3x-x^4+a^2x^2-ax^3

Answer 1

Answer:

${a}^{3} x - {x}^{4} + {a}^{2} {x}^{2} - a {x}^{3} \\ = ( - {x}^{4} ) (1 + ( \frac{ - a}{x} ) + ( \frac{ - a}{ x} ) {}^{2} + ( \frac{ - a}{x} ) {}^{3} )$

As you can see it's a GP

$- {x}^{4} ( \frac{ (\frac{ - a}{x}) {}^{4} - 1 }{ \frac{ - a}{x} - 1} ) = \frac{ {x}^{3}( {a}^{4} - {x}^{4} ) }{a + {x}^{3} } = \frac{ {x}^{3} ( {x}^{2} + {a}^{2})( a - x)(a + x) }{ {x}^{3} + a}$