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উৎপাদকে বিশ্লেষণ কর: $x^4-6x^2y^2+y^4$

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উৎপাদকে বিশ্লেষণ কর: $x^4-6x^2y^2+y^4$

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$x^4-6x^2y^2+y^4$

$=(x^2)^2-2 \cdot x^2 \cdot y^2+ (y^2)^2-4x^2y^2$

$=(x^2-y^2)^2 - (2xy)^2$

$=\{(x^2-y^2) + 2xy\}\{(x^2-y^2) - 2xy\}$

$=(x^2-y^2 + 2xy)(x^2-y^2 - 2xy)$

$=(x^2 + 2xy - y^2)(x^2 - 2xy - y^2)$ [Answer]
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Rules Applied:

  • $a^2-2ab+b^2=(a-b)^2$
  • $a^2-b^2=(a+b)(a-b)$

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