Question

question:
${x}^{8} - {16y}^{8} = ?$
the answer of this question will be :
$( {x}^{2} + 2xy + 2 {y}^{2} )( {x}^{2} - 2xy + 2 {y}^{2} )( {x}^{2} + 2 {y}^{2} )( {x}^{2} - 2 {y}^{2} )$
- : PROVE IT STEP BY STEP : -​

Answer 1

Question :-

Factorise :- ${x}^{8} \: - \: {16y}^{8}$

Answer :-

${x}^{8} \: - \: {16y}^{8}$

$\implies \: { {(x}^{4} )}^{2} \: - \: { {(4y}^{4}) }^{2}$

Applying Difference of two Square Formula,

$\implies \: ( {x}^{4} \: + \: {4y}^{4} ) \: ( {x}^{4} \: - \: {4y}^{4} )$

Now again factorising : ${x}^{4} \: - \: 4 {y}^{4}$

$\implies \: ( {x}^{2} \: + \: {2y}^{2} ) \: ( {x}^{2} \: - \: 2 {y}^{2} )$

So, the final solution is -

$\implies \: ( {x}^{4} \: + \: {y}^{4} ) \: ( {x}^{2} \: + \: 2 {y}^{2} ) \: ( {x}^{2} \: - \: 2 {y}^{2} )$

Step-by-step explanation:

HOPE IT HELPS !! : )