Mister Exam
Factor -y^2+y*a+2*a^2 squared
The solution
You have entered
[src]
2 2 - y + y*a + 2*a
$$2 a^{2} + \left(a y - y^{2}\right)$$
-y^2 + y*a + 2*a^2
The perfect square
Let's highlight the perfect square of the square three-member
$$2 a^{2} + \left(a y - y^{2}\right)$$
Let us write down the identical expression
$$2 a^{2} + \left(a y - y^{2}\right) = - \frac{9 y^{2}}{8} + \left(2 a^{2} + a y + \frac{y^{2}}{8}\right)$$
or
$$2 a^{2} + \left(a y - y^{2}\right) = - \frac{9 y^{2}}{8} + \left(\sqrt{2} a + \frac{\sqrt{2} y}{4}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{9}{8}} y + \left(\sqrt{2} a + \frac{\sqrt{2}}{4} y\right)\right) \left(\sqrt{\frac{9}{8}} y + \left(\sqrt{2} a + \frac{\sqrt{2}}{4} y\right)\right)$$
$$\left(- \frac{3 \sqrt{2}}{4} y + \left(\sqrt{2} a + \frac{\sqrt{2}}{4} y\right)\right) \left(\frac{3 \sqrt{2}}{4} y + \left(\sqrt{2} a + \frac{\sqrt{2}}{4} y\right)\right)$$
$$\left(\sqrt{2} a + y \left(- \frac{3 \sqrt{2}}{4} + \frac{\sqrt{2}}{4}\right)\right) \left(\sqrt{2} a + y \left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2}}{4}\right)\right)$$
$$\left(\sqrt{2} a - \frac{\sqrt{2} y}{2}\right) \left(\sqrt{2} a + \sqrt{2} y\right)$$
$$2 a^{2} + \left(a y - y^{2}\right)$$
Let us write down the identical expression
$$2 a^{2} + \left(a y - y^{2}\right) = - \frac{9 y^{2}}{8} + \left(2 a^{2} + a y + \frac{y^{2}}{8}\right)$$
or
$$2 a^{2} + \left(a y - y^{2}\right) = - \frac{9 y^{2}}{8} + \left(\sqrt{2} a + \frac{\sqrt{2} y}{4}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{9}{8}} y + \left(\sqrt{2} a + \frac{\sqrt{2}}{4} y\right)\right) \left(\sqrt{\frac{9}{8}} y + \left(\sqrt{2} a + \frac{\sqrt{2}}{4} y\right)\right)$$
$$\left(- \frac{3 \sqrt{2}}{4} y + \left(\sqrt{2} a + \frac{\sqrt{2}}{4} y\right)\right) \left(\frac{3 \sqrt{2}}{4} y + \left(\sqrt{2} a + \frac{\sqrt{2}}{4} y\right)\right)$$
$$\left(\sqrt{2} a + y \left(- \frac{3 \sqrt{2}}{4} + \frac{\sqrt{2}}{4}\right)\right) \left(\sqrt{2} a + y \left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2}}{4}\right)\right)$$
$$\left(\sqrt{2} a - \frac{\sqrt{2} y}{2}\right) \left(\sqrt{2} a + \sqrt{2} y\right)$$
Factorization
[src]
/ y\
(a + y)*|a - -|
\ 2/
$$\left(a - \frac{y}{2}\right) \left(a + y\right)$$
(a + y)*(a - y/2)
Combinatorics
[src]
-(a + y)*(y - 2*a)
$$- \left(- 2 a + y\right) \left(a + y\right)$$
-(a + y)*(y - 2*a)
Combining rational expressions
[src]
2 2*a + y*(a - y)
$$2 a^{2} + y \left(a - y\right)$$
2*a^2 + y*(a - y)