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Show that (3x – 2y)^2 + 24xy = (3x + 2y)^2.

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Show that (3x – 2y)2 + 24xy = (3x + 2y)2.

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LHS

(3x – 2y)2 + 24xy

= [(3x)2 – 2(3x) (2y) + (2y)2] + 24xy

= (9x2 – 12xy + 4y2) + 24xy

= 9x2 – 12xy + 24xy + 4y2

= 9x2 + 12xy + 4y2

= (3x)2 + 2 (3x) (2y) + (2y)2

= (3x + 2y)2 (Using identity I)

= RHS

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