Question

If $m=9x^2-4xy+5y^2$ and $n=-3x^2+2xy-y^2,$
find: (ii) 𝑚+2𝑛

Answer 1

Step: Putting the value of m and n in required equation $m=9x^2-4xy+5y^2$
and $n=-3x^2+2xy-y^2$
Then, $2n=2[-3x^2+2xy-y^2]$
$=-6x^2+4xy-2y^2$
$\Rightarrow m+2n=9x^2-4xy+5y^2+(-6x^2+4xy-2y^2)$
$=9x^2-6x^2-4xy+4xy+5y^2-2y^2$
$=3x^2+3y^2$
Hence, the answer is $3x^2+3y^2.$