x3 + 6x2y + 11xy2 + 6y3 এর উৎপাদক নিচের কোনটি?
Solution
Correct Answer: Option A
x3 + 6x2y + 11xy2 + 6y3
= x3 + 3 . x2 . 2y + 3 . x . (2y)2 + (2y)3 - xy2 - 2y3
= (x + 2y)3 - y2 (x + 2y)
= (x + 2y) {(x + 2y)2 - y2}
= (x + 2y)(x + 2y + y)(x + 2y - y)
= (x + y)(x + 2y)(x + 3y)
= x3 + 3 . x2 . 2y + 3 . x . (2y)2 + (2y)3 - xy2 - 2y3
= (x + 2y)3 - y2 (x + 2y)
= (x + 2y) {(x + 2y)2 - y2}
= (x + 2y)(x + 2y + y)(x + 2y - y)
= (x + y)(x + 2y)(x + 3y)
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