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