Question

Factorise:- Sin^8 theata-cos^8 theata

Answer 1

The answer is

$({ \sin {}^{4} (theta) }^{} + { \cos {}^{4} (theta) }^{}) ({ \sin {}^{4} (theta) }^{} - { \cos {}^{4} (theta) }^{})$

Please refer the above photograph for the used process.


KEY POINTS TO REMEMBER :-

☸️ a²-b²=(a+b) (a-b)


☸️
${( {x}^{m} )}^{n} = {x}^{mn}$

☸️ In factorization :-
One should look for identities. Then, following the identities one should solve the question.

Common identities found are :-

☸️ (a+b) ²=a²+b²+2ab

☸️ (a-b) ²=a²+b²-2ab

☸️ (a+b) ³ = a³+b³+3ab(a+b)

☸️ a²-b² =(a+b) (a-b)

☸️ a³+b³ = (a+b) +(a²-ab+b²)


Thanks!