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Expression simplification/ Factor perfect squares/ y^2+13*y*a-9*a^2

Factor y^2+13*y*a-9*a^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2               2
y  + 13*y*a - 9*a
$$- 9 a^{2} + \left(a 13 y + y^{2}\right)$$ 
y^2 + (13*y)*a - 9*a^2
General simplification [src] 
 2      2         
y  - 9*a  + 13*a*y
$$- 9 a^{2} + 13 a y + y^{2}$$ 
y^2 - 9*a^2 + 13*a*y
The perfect square
Let's highlight the perfect square of the square three-member
$$- 9 a^{2} + \left(a 13 y + y^{2}\right)$$
Let us write down the identical expression
$$- 9 a^{2} + \left(a 13 y + y^{2}\right) = \frac{205 y^{2}}{36} + \left(- 9 a^{2} + 13 a y - \frac{169 y^{2}}{36}\right)$$
or
$$- 9 a^{2} + \left(a 13 y + y^{2}\right) = \frac{205 y^{2}}{36} - \left(3 a - \frac{13 y}{6}\right)^{2}$$
Factorization [src] 
/      /       _____\\ /      /       _____\\
|    y*\13 - \/ 205 /| |    y*\13 + \/ 205 /|
|a - ----------------|*|a - ----------------|
\           18       / \           18       /
$$\left(a - \frac{y \left(13 - \sqrt{205}\right)}{18}\right) \left(a - \frac{y \left(13 + \sqrt{205}\right)}{18}\right)$$ 
(a - y*(13 - sqrt(205))/18)*(a - y*(13 + sqrt(205))/18)
Numerical answer [src] 
y^2 - 9.0*a^2 + 13.0*a*y
y^2 - 9.0*a^2 + 13.0*a*y
Assemble expression [src] 
 2      2         
y  - 9*a  + 13*a*y
$$- 9 a^{2} + 13 a y + y^{2}$$ 
y^2 - 9*a^2 + 13*a*y
Common denominator [src] 
 2      2         
y  - 9*a  + 13*a*y
$$- 9 a^{2} + 13 a y + y^{2}$$ 
y^2 - 9*a^2 + 13*a*y
Rational denominator [src] 
 2      2         
y  - 9*a  + 13*a*y
$$- 9 a^{2} + 13 a y + y^{2}$$ 
y^2 - 9*a^2 + 13*a*y
Combining rational expressions [src] 
     2               
- 9*a  + y*(y + 13*a)
$$- 9 a^{2} + y \left(13 a + y\right)$$ 
-9*a^2 + y*(y + 13*a)
Trigonometric part [src] 
 2      2         
y  - 9*a  + 13*a*y
$$- 9 a^{2} + 13 a y + y^{2}$$ 
y^2 - 9*a^2 + 13*a*y
Powers [src] 
 2      2         
y  - 9*a  + 13*a*y
$$- 9 a^{2} + 13 a y + y^{2}$$ 
y^2 - 9*a^2 + 13*a*y
Combinatorics [src] 
 2      2         
y  - 9*a  + 13*a*y
$$- 9 a^{2} + 13 a y + y^{2}$$ 
y^2 - 9*a^2 + 13*a*y
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