Question

simplify (x-2y+3) square +(x+2y-3) square​

Answer 1

Answer:

(x-2y+3)² + (x+2y-3)²

By using identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

= {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]}

= {x² + 4y² + 9 + -4xy + -12y + 6x} + {x² + 4y² + 9 + 4xy + -12y + -6x}

GROUP THE LIKE TERMS

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

-4xy and 4xy & 6x and -6x will get cancelled

= 2x² + 8y² + 18 + -24y

HOPE THIS HELPS.... :)

Answer 2

Given:

$(\mathrm{x}-2 \mathrm{y}+3)^{2}+(\mathrm{x}+2 \mathrm{y}-3)^{2}$

On simplification , we get

$\begin{array}{l}\Longrightarrow 2(\mathrm{x})^{2}+8 \mathrm{y}^{2}+2(3)^{2}+2 \cdot(\mathrm{x})(-2 \mathrm{y})+2 \cdot(-2 \mathrm{y})(3)+2 .(\mathrm{x})(3)+2 \cdot(\mathrm{x})(2 \mathrm{y})+ \\2 .(2 \mathrm{y})(-3)+2 \cdot(-3)(\mathrm{x})\end{array}$

$\Longrightarrow 2 \mathrm{x}^{2}+8 \mathrm{y}^{2}+18-24 \mathrm{y}$

Hence the answer is

$2 x^{2}+8 y^{2}+18-24 y$