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प्रश्न
Expand using the formula:
(4x + 2y + 3) (4x + 2y − 3)
योग
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उत्तर
(4x + 2y + 3)(4x + 2y − 3)
= (4x + 2y) (4x + 2y − 3) + 3(4x + 2y − 3)
= [(4x + 2y) (4x + 2y) − (4x + 2y)(3)] + [3(4x) + 3(2y) + 3(−3)]
= [(4x + 2y)2 − 12x − 6y] + [12x + 6y − 9]
= [(4x)2 + 2(4x × 2y) + (2y)2] − 12x − 6y + [12x + 6y − 9] ...{For (3x + 5y)2 using (a + b)2 = a2 + 2ab + b2}
= [16x2 + 2(8xy) + 4y2 − 12x − 6y] + [12x + 6y − 9]
= 16x2 + 16xy + 4y2 − 12x − 6y + 12x + 6y − 9
= 16x2 + 16xy + 4y2 − 0 + 0 − 9 ...{Here, −12x + 12x = 0 and −6y + 6y = 0}
∴ (4x + 2y + 3)(4x + 2y − 3) = 16x2 + 16xy + 4y2 − 9
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