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Expression simplification/ Factor perfect squares/ -y^2-9*y*p+7*p^2

Factor -y^2-9*y*p+7*p^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2              2
- y  - 9*y*p + 7*p
$$7 p^{2} + \left(- p 9 y - y^{2}\right)$$ 
-y^2 - 9*y*p + 7*p^2
The perfect square
Let's highlight the perfect square of the square three-member
$$7 p^{2} + \left(- p 9 y - y^{2}\right)$$
Let us write down the identical expression
$$7 p^{2} + \left(- p 9 y - y^{2}\right) = - \frac{109 y^{2}}{28} + \left(7 p^{2} - 9 p y + \frac{81 y^{2}}{28}\right)$$
or
$$7 p^{2} + \left(- p 9 y - y^{2}\right) = - \frac{109 y^{2}}{28} + \left(\sqrt{7} p - \frac{9 \sqrt{7} y}{14}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{109}{28}} y + \left(\sqrt{7} p + - \frac{9 \sqrt{7}}{14} y\right)\right) \left(\sqrt{\frac{109}{28}} y + \left(\sqrt{7} p + - \frac{9 \sqrt{7}}{14} y\right)\right)$$
$$\left(- \frac{\sqrt{763}}{14} y + \left(\sqrt{7} p + - \frac{9 \sqrt{7}}{14} y\right)\right) \left(\frac{\sqrt{763}}{14} y + \left(\sqrt{7} p + - \frac{9 \sqrt{7}}{14} y\right)\right)$$
$$\left(\sqrt{7} p + y \left(- \frac{9 \sqrt{7}}{14} + \frac{\sqrt{763}}{14}\right)\right) \left(\sqrt{7} p + y \left(- \frac{\sqrt{763}}{14} - \frac{9 \sqrt{7}}{14}\right)\right)$$
$$\left(\sqrt{7} p + y \left(- \frac{9 \sqrt{7}}{14} + \frac{\sqrt{763}}{14}\right)\right) \left(\sqrt{7} p + y \left(- \frac{\sqrt{763}}{14} - \frac{9 \sqrt{7}}{14}\right)\right)$$
General simplification [src] 
   2      2        
- y  + 7*p  - 9*p*y
$$7 p^{2} - 9 p y - y^{2}$$ 
-y^2 + 7*p^2 - 9*p*y
Factorization [src] 
/      /      _____\\ /      /      _____\\
|    y*\9 - \/ 109 /| |    y*\9 + \/ 109 /|
|p - ---------------|*|p - ---------------|
\           14      / \           14      /
$$\left(p - \frac{y \left(9 - \sqrt{109}\right)}{14}\right) \left(p - \frac{y \left(9 + \sqrt{109}\right)}{14}\right)$$ 
(p - y*(9 - sqrt(109))/14)*(p - y*(9 + sqrt(109))/14)
Trigonometric part [src] 
   2      2        
- y  + 7*p  - 9*p*y
$$7 p^{2} - 9 p y - y^{2}$$ 
-y^2 + 7*p^2 - 9*p*y
Powers [src] 
   2      2        
- y  + 7*p  - 9*p*y
$$7 p^{2} - 9 p y - y^{2}$$ 
-y^2 + 7*p^2 - 9*p*y
Assemble expression [src] 
   2      2        
- y  + 7*p  - 9*p*y
$$7 p^{2} - 9 p y - y^{2}$$ 
-y^2 + 7*p^2 - 9*p*y
Combinatorics [src] 
   2      2        
- y  + 7*p  - 9*p*y
$$7 p^{2} - 9 p y - y^{2}$$ 
-y^2 + 7*p^2 - 9*p*y
Rational denominator [src] 
   2      2        
- y  + 7*p  - 9*p*y
$$7 p^{2} - 9 p y - y^{2}$$ 
-y^2 + 7*p^2 - 9*p*y
Numerical answer [src] 
-y^2 + 7.0*p^2 - 9.0*p*y
-y^2 + 7.0*p^2 - 9.0*p*y
Combining rational expressions [src] 
   2               
7*p  + y*(-y - 9*p)
$$7 p^{2} + y \left(- 9 p - y\right)$$ 
7*p^2 + y*(-y - 9*p)
Common denominator [src] 
   2      2        
- y  + 7*p  - 9*p*y
$$7 p^{2} - 9 p y - y^{2}$$ 
-y^2 + 7*p^2 - 9*p*y
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