Mister Exam
Factor -y^2-13*y*a-4*a^2 squared
The solution
You have entered
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2 2 - y - 13*y*a - 4*a
$$- 4 a^{2} + \left(- a 13 y - y^{2}\right)$$
-y^2 - 13*y*a - 4*a^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- 4 a^{2} + \left(- a 13 y - y^{2}\right)$$
Let us write down the identical expression
$$- 4 a^{2} + \left(- a 13 y - y^{2}\right) = \frac{153 y^{2}}{16} + \left(- 4 a^{2} - 13 a y - \frac{169 y^{2}}{16}\right)$$
or
$$- 4 a^{2} + \left(- a 13 y - y^{2}\right) = \frac{153 y^{2}}{16} - \left(2 a + \frac{13 y}{4}\right)^{2}$$
$$- 4 a^{2} + \left(- a 13 y - y^{2}\right)$$
Let us write down the identical expression
$$- 4 a^{2} + \left(- a 13 y - y^{2}\right) = \frac{153 y^{2}}{16} + \left(- 4 a^{2} - 13 a y - \frac{169 y^{2}}{16}\right)$$
or
$$- 4 a^{2} + \left(- a 13 y - y^{2}\right) = \frac{153 y^{2}}{16} - \left(2 a + \frac{13 y}{4}\right)^{2}$$
Factorization
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/ / ____\\ / / ____\\ | y*\-13 + 3*\/ 17 /| | y*\13 + 3*\/ 17 /| |a - ------------------|*|a + -----------------| \ 8 / \ 8 /
$$\left(a - \frac{y \left(-13 + 3 \sqrt{17}\right)}{8}\right) \left(a + \frac{y \left(3 \sqrt{17} + 13\right)}{8}\right)$$
(a - y*(-13 + 3*sqrt(17))/8)*(a + y*(13 + 3*sqrt(17))/8)
General simplification
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2 2 - y - 4*a - 13*a*y
$$- 4 a^{2} - 13 a y - y^{2}$$
-y^2 - 4*a^2 - 13*a*y
Combining rational expressions
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2 - 4*a + y*(-y - 13*a)
$$- 4 a^{2} + y \left(- 13 a - y\right)$$
-4*a^2 + y*(-y - 13*a)
Assemble expression
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2 2 - y - 4*a - 13*a*y
$$- 4 a^{2} - 13 a y - y^{2}$$
-y^2 - 4*a^2 - 13*a*y
Common denominator
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2 2 - y - 4*a - 13*a*y
$$- 4 a^{2} - 13 a y - y^{2}$$
-y^2 - 4*a^2 - 13*a*y
Rational denominator
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2 2 - y - 4*a - 13*a*y
$$- 4 a^{2} - 13 a y - y^{2}$$
-y^2 - 4*a^2 - 13*a*y
Trigonometric part
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2 2 - y - 4*a - 13*a*y
$$- 4 a^{2} - 13 a y - y^{2}$$
-y^2 - 4*a^2 - 13*a*y