Mister Exam
Factor -y^2-y*q-4*q^2 squared
The solution
You have entered
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2 2 - y - y*q - 4*q
$$- 4 q^{2} + \left(- q y - y^{2}\right)$$
-y^2 - y*q - 4*q^2
Factorization
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/ / ____\\ / / ____\\ | y*\-1 + I*\/ 15 /| | y*\1 + I*\/ 15 /| |q - -----------------|*|q + ----------------| \ 8 / \ 8 /
$$\left(q - \frac{y \left(-1 + \sqrt{15} i\right)}{8}\right) \left(q + \frac{y \left(1 + \sqrt{15} i\right)}{8}\right)$$
(q - y*(-1 + i*sqrt(15))/8)*(q + y*(1 + i*sqrt(15))/8)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 4 q^{2} + \left(- q y - y^{2}\right)$$
Let us write down the identical expression
$$- 4 q^{2} + \left(- q y - y^{2}\right) = - \frac{15 y^{2}}{16} + \left(- 4 q^{2} - q y - \frac{y^{2}}{16}\right)$$
or
$$- 4 q^{2} + \left(- q y - y^{2}\right) = - \frac{15 y^{2}}{16} - \left(2 q + \frac{y}{4}\right)^{2}$$
$$- 4 q^{2} + \left(- q y - y^{2}\right)$$
Let us write down the identical expression
$$- 4 q^{2} + \left(- q y - y^{2}\right) = - \frac{15 y^{2}}{16} + \left(- 4 q^{2} - q y - \frac{y^{2}}{16}\right)$$
or
$$- 4 q^{2} + \left(- q y - y^{2}\right) = - \frac{15 y^{2}}{16} - \left(2 q + \frac{y}{4}\right)^{2}$$
Combining rational expressions
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2 - 4*q + y*(-q - y)
$$- 4 q^{2} + y \left(- q - y\right)$$
-4*q^2 + y*(-q - y)