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Question
Show that (x + 2y)2 – (x – 2y)2 = 8xy
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Solution
L.H.S = (x + 2y)2 – (x – 2y)2
= x2 + (2 × x × 2y) + (2y)2 – [x2 – (2 × x × 2y) + (2y)2]
= x2 + 4xy + 4y2 – [x2 – 4xy + 22y2]
= x2 + 4xy + 4y2 – x2 + 4xy – 4y2
= x2 – x2 + 4xy + 4xy + 4y2 – 4y2
= x2(1 – 1) + xy(4 + 4) + y2(4 – 4)
= 0x2 + 8xy + 0y2
= 8xy
= R.H.S
∴ (x + 2y)2 – (x – 2y)2 = 8xy ...[∵ (a + b)2 = a2 + 2ab + b2 and (a – b)2 = a2 – 2ab + b2]
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