factorize:
x^16 - y^16
Answers
Step-by-step explanation:
bhai
solution tu hi de de
Answer:
x
16
−y
16
=(x
8
)
2
−(y
8
)
2
=(x
8
+y
8
)(x
8
−y
8
)
\boxed {\pink { Since, a^{2} - b^{2} = ( a + b )( a - b ) }}
Since,a
2
−b
2
=(a+b)(a−b)
= ( x^{8} + y^{8} )[ (x^{4})^{2} - (y^{4})^{2} ]=(x
8
+y
8
)[(x
4
)
2
−(y
4
)
2
]
= ( x^{8} + y^{8} ) (x^{4} + y^{4}) ( x^{4} - y^{4} )=(x
8
+y
8
)(x
4
+y
4
)(x
4
−y
4
)
= ( x^{8} + y^{8} ) (x^{4} + y^{4}) [ (x^{2})^{2} - (y^{2} )^{2}]=(x
8
+y
8
)(x
4
+y
4
)[(x
2
)
2
−(y
2
)
2
]
= ( x^{8} + y^{8} ) (x^{4} + y^{4}) (x^{2} + y^{2} )( x^{2} - y^{2} )=(x
8
+y
8
)(x
4
+y
4
)(x
2
+y
2
)(x
2
−y
2
)
= ( x^{8} + y^{8} ) (x^{4} + y^{4}) (x^{2} + y^{2} )(x + y )( x- y)=(x
8
+y
8
)(x
4
+y
4
)(x
2
+y
2
)(x+y)(x−y)
Therefore.,
\begin{gathered} \red { Factors \: of \: x^{16} - y^{16}}\\\green {= ( x^{8} + y^{8} ) (x^{4}+ y^{4}) (x^{2}
+ y^{2} )(x + y )( x- y)}\end{gathered}
Factorsofx
16
−y
16
=(x
8
+y
8
)(x
4
+y
4
)(x
2
+y
2
)(x+y)(x−y)
•••♪