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Mathematics
JAMB
Factorize: 16x
4
−y
4
A.
(2x−y)(2x+y)(4x
2
+y
2
)
B.
(2x+y)(2x+y)(4x
2
+y
2
)
C.
(2x−y)(2x−y)(4x
2
+y
2
)
D.
(2x−y)(2x+y)(4x
2
−y
2
)
Correct Answer:
(2x−y)(2x+y)(4x
2
+y
2
)
Explanation
16x
4
− y
4
= 2
4
x
4
− y
4
= (2x)
4
− y
4
= ((2x)
2
)
2
− (y
2
)
2
Using a
2
− b
2
= (a - b)(a + b) identity = ((2x)
2
−y
2
)((2x)
2
+y
2
) Using the identity one more time = (2x − y)(2x + y)((2x)
2
+ y
2
) ∴ (2x − y)(2x + y)(4x
2
+ y
2
)
16x
4
− y
4
= 2
4
x
4
− y
4
= (2x)
4
− y
4
= ((2x)
2
)
2
− (y
2
)
2
Using a
2
− b
2
= (a - b)(a + b) identity = ((2x)
2
−y
2
)((2x)
2
+y
2
) Using the identity one more time = (2x − y)(2x + y)((2x)
2
+ y
2
) ∴ (2x − y)(2x + y)(4x
2
+ y
2
)
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