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Question
Expand using the formula:
(3x + 5y + 2) (3x + 5y − 2)
Sum
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Solution
(3x + 5y + 2) (3x + 5y − 2)
= (3x + 5y) (3x + 5y − 2) + 2(3x + 5y − 2)
= (3x + 5y) (3x + 5y) − (3x + 5y) (2) + [2(3x) + 2(5y) 2(−2)]
= (3x + 5y)2 − 6x − 10y + (6x + 10y − 4)
= [(3x)2 + 2(3x × 5y) + (5y)2] − 6x − 10y + (6x + 10y − 4) ...{For (3x + 5y)2 using (a + b)2 = a2 + 2ab + b2}
= 9x2 + 2(15xy) + 25y2 − 6x − 10y + (6x + 10y − 4)
= 9x2 + 30xy + 25y2 − 6x − 10y + 6x + 10y − 4
= 9x2 + 30xy + 25y2 − 0 + 0 − 4 ...{Here, −6x + 6x = 0 and −10y + 10y = 0}
∴ (3x + 5y + 2) (3x + 5y − 2) = 9x2 + 30xy + 25y2 − 4
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