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Question
Simplify.
(x − 2y +3)2 + (x + 2y − 3)2
Solution
It is known that,
\[\left( a + b + c \right)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\]
\[\ \left( x - 2y + 3 \right)^2 + \left( x + 2y - 3 \right)^2 \]
\[ = \left( x \right)^2 + \left( - 2y \right)^2 + \left( 3 \right)^2 + 2 \times x \times \left( - 2y \right) + 2 \times \left( - 2y \right) \times 3 + 2 \times 3 \times x + \left( x \right)^2 + \left( 2y \right)^2 + \left( - 3 \right)^2 + 2 \times x \times 2y + 2 \times \left( 2y \right) \times \left( - 3 \right) + 2 \times \left( - 3 \right) \times x\]
\[ = x^2 + 4 y^2 + 9 - 4xy - 12y + 6x + x^2 + 4 y^2 + 9 + 4xy - 12y - 6x\]
\[ = 2 x^2 + 8 y^2 + 18 - 24y\]
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