The perimeter of a triangle is $8 y^{2} - 9 y + 4$ and its two sides are $3 y^{2} - 5 y$ and $4 y^{2} + 12$ , then its third sides is $y^{m} - 4 y - 8$ .
Value of $m$ is

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Solution

Perimeter is equal to the sum of sides,
Let A be the third side,
We can directly add the coefficients of like variables,
$3 y^{2} - 5 y + 4 y^{2} + 12 + A = 8 y^{2} - 9 y + 4$
$A = 8 y^{2} - 9 y + 4 - (3 y^{2} - 5 y + 4 y^{2} + 12)$
$= y^{2} - 4 y - 8$

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