(a2 - b2) (x2 - y2) + 4abxy এর উৎপাদক কত?
Solution
Correct Answer: Option B
(a2 - b2) (x2 - y2) + 4abxy
= a2x2 − a2y2 − b2x2 + b2y2 + 4abxy
= a2x2 + b2y2 + 2abxy − a2y2 − b2x2 + 2abxy
= a2x2 + b2y2 + 2abxy − (a2y2 + b2x2 - 2abxy)
= (ax + by)2 - (ay − bx)2
= [(ax + by) + (ay − bx)] [(ax + by) − (ay − bx)]
= (ax + by + ay − bx) (ax + by − ay + bx)
= a2x2 − a2y2 − b2x2 + b2y2 + 4abxy
= a2x2 + b2y2 + 2abxy − a2y2 − b2x2 + 2abxy
= a2x2 + b2y2 + 2abxy − (a2y2 + b2x2 - 2abxy)
= (ax + by)2 - (ay − bx)2
= [(ax + by) + (ay − bx)] [(ax + by) − (ay − bx)]
= (ax + by + ay − bx) (ax + by − ay + bx)
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