Mister Exam

Other calculators

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

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

An expression to simplify:

The solution

You have entered [src] 
 2              2
y  - 9*y*a - 2*a
$$- 2 a^{2} + \left(- a 9 y + y^{2}\right)$$ 
y^2 - 9*y*a - 2*a^2
General simplification [src] 
 2      2        
y  - 2*a  - 9*a*y
$$- 2 a^{2} - 9 a y + y^{2}$$ 
y^2 - 2*a^2 - 9*a*y
Factorization [src] 
/      /       ____\\ /      /      ____\\
|    y*\-9 + \/ 89 /| |    y*\9 + \/ 89 /|
|a - ---------------|*|a + --------------|
\           4       / \          4       /
$$\left(a - \frac{y \left(-9 + \sqrt{89}\right)}{4}\right) \left(a + \frac{y \left(9 + \sqrt{89}\right)}{4}\right)$$ 
(a - y*(-9 + sqrt(89))/4)*(a + y*(9 + sqrt(89))/4)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 2 a^{2} + \left(- a 9 y + y^{2}\right)$$
Let us write down the identical expression
$$- 2 a^{2} + \left(- a 9 y + y^{2}\right) = \frac{89 y^{2}}{8} + \left(- 2 a^{2} - 9 a y - \frac{81 y^{2}}{8}\right)$$
or
$$- 2 a^{2} + \left(- a 9 y + y^{2}\right) = \frac{89 y^{2}}{8} - \left(\sqrt{2} a + \frac{9 \sqrt{2} y}{4}\right)^{2}$$
Trigonometric part [src] 
 2      2        
y  - 2*a  - 9*a*y
$$- 2 a^{2} - 9 a y + y^{2}$$ 
y^2 - 2*a^2 - 9*a*y
Assemble expression [src] 
 2      2        
y  - 2*a  - 9*a*y
$$- 2 a^{2} - 9 a y + y^{2}$$ 
y^2 - 2*a^2 - 9*a*y
Rational denominator [src] 
 2      2        
y  - 2*a  - 9*a*y
$$- 2 a^{2} - 9 a y + y^{2}$$ 
y^2 - 2*a^2 - 9*a*y
Combining rational expressions [src] 
     2              
- 2*a  + y*(y - 9*a)
$$- 2 a^{2} + y \left(- 9 a + y\right)$$ 
-2*a^2 + y*(y - 9*a)
Common denominator [src] 
 2      2        
y  - 2*a  - 9*a*y
$$- 2 a^{2} - 9 a y + y^{2}$$ 
y^2 - 2*a^2 - 9*a*y
Combinatorics [src] 
 2      2        
y  - 2*a  - 9*a*y
$$- 2 a^{2} - 9 a y + y^{2}$$ 
y^2 - 2*a^2 - 9*a*y
Powers [src] 
 2      2        
y  - 2*a  - 9*a*y
$$- 2 a^{2} - 9 a y + y^{2}$$ 
y^2 - 2*a^2 - 9*a*y
Numerical answer [src] 
y^2 - 2.0*a^2 - 9.0*a*y
y^2 - 2.0*a^2 - 9.0*a*y
    © Mister Exam – Calculator