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Simplify: (3x + 2y)^2 + (3x – 2y)^2

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Simplify:

(3x + 2y)2 + (3x – 2y)2

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The given expression is (3x + 2y)2 + (3x – 2y)2

We have,

(3x + 2y)2 = (3x)2 + 2.3x.2y + (2y)2(Here we apply standard identities)

= 9x2 + 12xy + 4y2

and

(3x-2y)2 = (3x)2-2.3x.2y + (2y)2

= 9x2-12xy + 4y2

Therefore,

(3x + 2y)2 + (3x – 2y)2 = 9x2 + 12xy + 4y2 + 9x2-12xy + 4y2

= 18x2 + 8y2

= 2(9x2 + 4y2)

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