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উৎপাদকে বিশ্লেষণ কর: $a^2+6a+8-y^2+2y$

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উৎপাদকে বিশ্লেষণ কর: $a^2+6a+8-y^2+2y$

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$a^2+6a+8-y^2+2y$

$=a^2+6a+9-y^2+2y-1$

$=(a^2+6a+9)-(y^2-2y+1)$

$=(a^2+2 \cdot a \cdot 3 + 3^2)$$-(y^2-2 \cdot y \cdot 1 + 1^2)$

$=(a+ 3)^2-(y-1)^2$

$=\{(a+3)+(y-1)\}$$\{(a+3)-(y-1)\}$

$=(a+3+y-1)(a+3-y+1)$

$=(a+y+2)(a-y+4)$ [Answer]
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Rules Applied:

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

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