Q2 of 36 Page 28

Simplify

(x – 2y + 3)2 +(x + 2y – 3)2

(x – 2y + 3)2 +(x + 2y – 3)2 = [(x)2 +(- 2y)2 + (3)2 +{2 ×(x)×(- 2y)} +{2 ×(- 2y)× (3)} +{2 ×(x)×(3)} ] + [(x)2 +(2y)2 + (- 3)2 +{2×(x)×(2y)} +{2×(2y)×(- 3)} +{2 ×(x)×(-3)} ]


{ ∵(a + b +c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac }


= [ x2 + 4y2 + 9 + {– 4xy } +{– 12y } +{6x } ] + [ x2 + 4y2 + 9 +{4xy } +{– 12y } +{– 6x } ]


= [ x2 + 4y2 + 9 – 4xy – 12y + 6x ] + [ x2 + 4y2 + 9 + 4xy – 12y – 6x ]


= x2 + 4y2 + 9 – 4xy – 12y + 6x + x2 + 4y2 + 9 + 4xy – 12y – 6x


= 2x2 + 8y2 + 18 – 24y


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