2023
Mathematics
67ca00ce0c643c71d77dee1f
Factorize: 16x4−y4
A.
(2x−y)(2x+y)(4x2+y2)
B.
(2x+y)(2x+y)(4x2+y2)
C.
(2x−y)(2x−y)(4x2+y2)
D.
(2x−y)(2x+y)(4x2−y2)
Correct Answer: (2x−y)(2x+y)(4x2+y2)
Explanation
16x4 − y4 = 24x4 − y4 = (2x)4 − y4 = ((2x)2)2 − (y2)2 Using a2 − b2 = (a - b)(a + b) identity = ((2x)2−y2)((2x)2+y2) Using the identity one more time = (2x − y)(2x + y)((2x)2 + y2) ∴ (2x − y)(2x + y)(4x2 + y2)
16x4 − y4 = 24x4 − y4 = (2x)4 − y4 = ((2x)2)2 − (y2)2 Using a2 − b2 = (a - b)(a + b) identity = ((2x)2−y2)((2x)2+y2) Using the identity one more time = (2x − y)(2x + y)((2x)2 + y2) ∴ (2x − y)(2x + y)(4x2 + y2)THIS WEEK's
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