Question

factotise the following
${x}^{4} - (y - x) {}^{4}$
​

Answer 1

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

${x}^{4} - (y - x) {}^{4}$

Step by step explanation:

Here ,this identity is used:

$\bold{\pink{\boxed{{x}^{2} - {y}^{2} = (x + y)(x - y)}}}$

=>Here ,we split x^4 into x^2 and (y-x)^4 into (y-x)^2 so that our identity would be apply.

$= > { ({x}^{2}) }^{2} - {[{(y - x)}^{2} ]}^{2}$

$\bold{ = > ( {x}^{2} + y - x)( {x}^{2} - y + x)}$

Related Formulas:

$\bold{\boxed{ {(x ± y)}^{2} = {x}^{2} + {y}^{2} ±2xy}}$

$\bold{\boxed{{(x ±y)}^{3} = {x}^{3} + {y}^{3}±3xy(x±y)}}$

$\bold{\boxed{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}}$

$\bold{\boxed{ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy+ {y}^{2} )}}$