# How do you simplify  (97x^2-56xy+86y^2)-(-56x^2+53xy+93y^2)?

Jun 9, 2015

$153 {x}^{2} - 109 x y - 7 {y}^{2}$

#### Explanation:

$\left(97 {x}^{2} - 56 x y + 86 {y}^{2}\right) - \left(- 56 {x}^{2} + 53 x y + 93 {y}^{2}\right)$
$97 {x}^{2} - 56 x y + 86 {y}^{2} + 56 {x}^{2} - 53 x y - 93 {y}^{2}$
$97 {x}^{2} - 56 x y + 86 {y}^{2} + 56 {x}^{2} - 53 x y - 93 {y}^{2}$
$153 {x}^{2} - 109 x y - 7 {y}^{2}$
$\left(17 \cdot 9\right) {x}^{2} - 109 x y - 7 {y}^{2}$
If we would to reduce more, we could try to devide the trinomial into 2 parts as:
$\left(a x + b y\right) \left(c x + \mathrm{dy}\right)$
So the hard problem would become how to find a,b,c,d, if:
$b \cdot d = - 7$
$a \cdot c = 17 \cdot {3}^{2}$
$a \cdot d + b \cdot c = - 109$
But without any result.