Question

The sum of two expressions is
$5 {x}^{2} y + 2 {x}^{2} {y}^{2} + 4 {y}^{2} x$
If one of them is
$12 {x}^{2} y - 2 {x}^{2} {y}^{2} + 3 {y}^{2} x$
Find the other.​

Answer 1

Given:-

$\red{➤}\:$$\sf One\: Expression = 12 {x}^{2} y - 2 {x}^{2} {y}^{2} + 3 {y}^{2}x$

$\red{➤}\:$$\sf Sum\:of\: Expression = 5 {x}^{2} y + 2 {x}^{2} {y}^{2} +$

$\sf 4 {y}^{2} x$

To Find:-

$\orange{☛}\:$$\sf Other \: Expression$

Assumption:-

$\red{•}\:$$\sf{Let \;the\; other\; expression \:be\: \red{a}}$

Solution:-

$\underline{\tt{Now,}}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf 12 {x}^{2} y - 2 {x}^{2} {y}^{2} + 3 {y}^{2} x + a =5 {x}^{2} y + 2 {x}^{2} {y}^{2} + 4 {y}^{2} x \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf a =5 {x}^{2} y + 2 {x}^{2} {y}^{2} + 4 {y}^{2} x - 12 {x}^{2} y - 2 {x}^{2} {y}^{2} + 3 {y}^{2} x \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf a =5 {x}^{2} y + 2 {x}^{2} {y}^{2} + 4 {y}^{2} x -( 12 {x}^{2} y - 2 {x}^{2} {y}^{2} + 3 {y}^{2} x) \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf a =5 {x}^{2} y + 2 {x}^{2} {y}^{2} + 4 {y}^{2} x -12 {x}^{2} y + 2 {x}^{2} {y}^{2} - 3 {y}^{2} x \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf a =5 {x}^{2} y-12 {x}^{2} y + 2 {x}^{2} {y}^{2} + 2 {x}^{2} {y}^{2} + 4 {y}^{2} x - 3 {y}^{2} x \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf a =-7 {x}^{2} y+ 4 {x}^{2} {y}^{2} + {y}^{2} x \\\end{gathered}$

$\boxed{\sf{Other \: Expression \implies \red{ -7 {x}^{2} y+ 4 {x}^{2} {y}^{2} + {y}^{2} x}}}$

Note-

• Only Like algebraic terms can be added.
• Change of signs of term after opening of brackets before negetive sign.
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