Mister Exam
Factor -y^2-2*y*t-4*t^2 squared
The solution
You have entered
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2 2 - y - 2*y*t - 4*t
$$- 4 t^{2} + \left(- t 2 y - y^{2}\right)$$
-y^2 - 2*y*t - 4*t^2
General simplification
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2 2 - y - 4*t - 2*t*y
$$- 4 t^{2} - 2 t y - y^{2}$$
-y^2 - 4*t^2 - 2*t*y
Factorization
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/ / ___\\ / / ___\\ | y*\-1 + I*\/ 3 /| | y*\1 + I*\/ 3 /| |t - ----------------|*|t + ---------------| \ 4 / \ 4 /
$$\left(t - \frac{y \left(-1 + \sqrt{3} i\right)}{4}\right) \left(t + \frac{y \left(1 + \sqrt{3} i\right)}{4}\right)$$
(t - y*(-1 + i*sqrt(3))/4)*(t + y*(1 + i*sqrt(3))/4)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 4 t^{2} + \left(- t 2 y - y^{2}\right)$$
Let us write down the identical expression
$$- 4 t^{2} + \left(- t 2 y - y^{2}\right) = - \frac{3 y^{2}}{4} + \left(- 4 t^{2} - 2 t y - \frac{y^{2}}{4}\right)$$
or
$$- 4 t^{2} + \left(- t 2 y - y^{2}\right) = - \frac{3 y^{2}}{4} - \left(2 t + \frac{y}{2}\right)^{2}$$
$$- 4 t^{2} + \left(- t 2 y - y^{2}\right)$$
Let us write down the identical expression
$$- 4 t^{2} + \left(- t 2 y - y^{2}\right) = - \frac{3 y^{2}}{4} + \left(- 4 t^{2} - 2 t y - \frac{y^{2}}{4}\right)$$
or
$$- 4 t^{2} + \left(- t 2 y - y^{2}\right) = - \frac{3 y^{2}}{4} - \left(2 t + \frac{y}{2}\right)^{2}$$
Combining rational expressions
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2 - 4*t + y*(-y - 2*t)
$$- 4 t^{2} + y \left(- 2 t - y\right)$$
-4*t^2 + y*(-y - 2*t)