Mister Exam
Factor 14*y^2+6*y*x+2*x^2 squared
The solution
You have entered
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2 2 14*y + 6*y*x + 2*x
$$2 x^{2} + \left(x 6 y + 14 y^{2}\right)$$
14*y^2 + (6*y)*x + 2*x^2
General simplification
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2 2 2*x + 14*y + 6*x*y
$$2 x^{2} + 6 x y + 14 y^{2}$$
2*x^2 + 14*y^2 + 6*x*y
Factorization
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/ / ____\\ / / ____\\ | y*\-3 + I*\/ 19 /| | y*\3 + I*\/ 19 /| |x - -----------------|*|x + ----------------| \ 2 / \ 2 /
$$\left(x - \frac{y \left(-3 + \sqrt{19} i\right)}{2}\right) \left(x + \frac{y \left(3 + \sqrt{19} i\right)}{2}\right)$$
(x - y*(-3 + i*sqrt(19))/2)*(x + y*(3 + i*sqrt(19))/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$2 x^{2} + \left(x 6 y + 14 y^{2}\right)$$
Let us write down the identical expression
$$2 x^{2} + \left(x 6 y + 14 y^{2}\right) = \frac{19 y^{2}}{2} + \left(2 x^{2} + 6 x y + \frac{9 y^{2}}{2}\right)$$
or
$$2 x^{2} + \left(x 6 y + 14 y^{2}\right) = \frac{19 y^{2}}{2} + \left(\sqrt{2} x + \frac{3 \sqrt{2} y}{2}\right)^{2}$$
$$2 x^{2} + \left(x 6 y + 14 y^{2}\right)$$
Let us write down the identical expression
$$2 x^{2} + \left(x 6 y + 14 y^{2}\right) = \frac{19 y^{2}}{2} + \left(2 x^{2} + 6 x y + \frac{9 y^{2}}{2}\right)$$
or
$$2 x^{2} + \left(x 6 y + 14 y^{2}\right) = \frac{19 y^{2}}{2} + \left(\sqrt{2} x + \frac{3 \sqrt{2} y}{2}\right)^{2}$$
Trigonometric part
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2 2 2*x + 14*y + 6*x*y
$$2 x^{2} + 6 x y + 14 y^{2}$$
2*x^2 + 14*y^2 + 6*x*y
Assemble expression
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2 2 2*x + 14*y + 6*x*y
$$2 x^{2} + 6 x y + 14 y^{2}$$
2*x^2 + 14*y^2 + 6*x*y
Rational denominator
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2 2 2*x + 14*y + 6*x*y
$$2 x^{2} + 6 x y + 14 y^{2}$$
2*x^2 + 14*y^2 + 6*x*y
Common denominator
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2 2 2*x + 14*y + 6*x*y
$$2 x^{2} + 6 x y + 14 y^{2}$$
2*x^2 + 14*y^2 + 6*x*y
Combining rational expressions
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/ 2 \ 2*\x + y*(3*x + 7*y)/
$$2 \left(x^{2} + y \left(3 x + 7 y\right)\right)$$
2*(x^2 + y*(3*x + 7*y))