Maharashtra State BoardSSC (English Medium) 8th Standard
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Simplify. (X − 2y +3)2 + (X + 2y − 3)2 - Mathematics

Sum

Simplify.

(x − 2y +3)2 + (x + 2y − 3)2

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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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APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 5 Expansion formulae
Practice Set 5.4 | Q 2.1 | Page 28
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