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ঘন-এর সাহায্যে সরল কর: $(7x+3b)^3$$-(5x+3b)^3$$-6x(7x+3b)(5x+3b)$

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$(7x+3b)^3-(5x+3b)^3-6x(7x+3b)(5x+3b)$

$=(7x+3b)^3-(5x+3b)^3-3\cdot(7x+3b)(5x+3b)\cdot2x$

ধরি,
$(7x+3b)=p$ এবং $(5x+3b)=q$

এখন,
$p-q$

$=(7x+3b)-(5x+3b)$

$=7x+3b-5x-3b$

$=2x$

সুতরাং পদত্ত রাশি দাঁড়ায়,
$p^3-p^3-3\cdot pq\cdot(p-q)$

$=p^3-p^3-3pq(p-q)$

$=(p-q)^3$

$=(2x)^3$

$=8x^3$ [Answer]

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