Mister Exam
Factor x^2+3*y*x+2*y^2 squared
The solution
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2 2 x + 3*y*x + 2*y
$$2 y^{2} + \left(x^{2} + x 3 y\right)$$
x^2 + (3*y)*x + 2*y^2
The perfect square
Let's highlight the perfect square of the square three-member
$$2 y^{2} + \left(x^{2} + x 3 y\right)$$
Let us write down the identical expression
$$2 y^{2} + \left(x^{2} + x 3 y\right) = - \frac{y^{2}}{4} + \left(x^{2} + 3 x y + \frac{9 y^{2}}{4}\right)$$
or
$$2 y^{2} + \left(x^{2} + x 3 y\right) = - \frac{y^{2}}{4} + \left(x + \frac{3 y}{2}\right)^{2}$$
in the view of the product
$$\left(- \frac{y}{2} + \left(x + \frac{3 y}{2}\right)\right) \left(\frac{y}{2} + \left(x + \frac{3 y}{2}\right)\right)$$
$$\left(- \frac{y}{2} + \left(x + \frac{3 y}{2}\right)\right) \left(\frac{y}{2} + \left(x + \frac{3 y}{2}\right)\right)$$
$$\left(x + y \left(- \frac{1}{2} + \frac{3}{2}\right)\right) \left(x + y \left(\frac{1}{2} + \frac{3}{2}\right)\right)$$
$$\left(x + y\right) \left(x + 2 y\right)$$
$$2 y^{2} + \left(x^{2} + x 3 y\right)$$
Let us write down the identical expression
$$2 y^{2} + \left(x^{2} + x 3 y\right) = - \frac{y^{2}}{4} + \left(x^{2} + 3 x y + \frac{9 y^{2}}{4}\right)$$
or
$$2 y^{2} + \left(x^{2} + x 3 y\right) = - \frac{y^{2}}{4} + \left(x + \frac{3 y}{2}\right)^{2}$$
in the view of the product
$$\left(- \frac{y}{2} + \left(x + \frac{3 y}{2}\right)\right) \left(\frac{y}{2} + \left(x + \frac{3 y}{2}\right)\right)$$
$$\left(- \frac{y}{2} + \left(x + \frac{3 y}{2}\right)\right) \left(\frac{y}{2} + \left(x + \frac{3 y}{2}\right)\right)$$
$$\left(x + y \left(- \frac{1}{2} + \frac{3}{2}\right)\right) \left(x + y \left(\frac{1}{2} + \frac{3}{2}\right)\right)$$
$$\left(x + y\right) \left(x + 2 y\right)$$
Combining rational expressions
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2 2*y + x*(x + 3*y)
$$x \left(x + 3 y\right) + 2 y^{2}$$
2*y^2 + x*(x + 3*y)