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प्रश्न
Find the product:
(5x + 4y + 2) (5x + 4y − 2)
योग
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उत्तर
(5x + 4y + 2) (5x + 4y − 2)
= (5x + 4y) (5x + 4y − 2) + 2(5x + 4y − 2)
= [(5x + 4y) (5x + 4y) − (5x + 4y)(2)] + [2(5x) + 2(4y) + 2(−2)]
= [(5x + 4y)2 − 10x − 8y] + [10x + 8y − 4]
= [(5x)2 + 2(5x × 4y) + (4y)2] − 10x − 8y + [10x + 8y − 4] ...{For (5x + 4y)2 using (a + b)2 = a2 + 2ab + b2}
= [25x2 + 2(20xy) + 16y2 − 10x − 8y] + [10x + 8y − 4]
= 25x2 + 40xy + 16y2 − 10x − 8y + 10x + 8y − 4
= 25x2 + 40xy + 16y2 − 0 + 0 − 4 ...{Here, −10x + 10x = 0 and −8y + 8y = 0}
∴ (5x + 4y + 3) (5x + 4y − 2) = 25x2 + 40xy + 16y2 − 4
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