Mister Exam
Factor 8*x^2-11*x*y+6*y^2 squared
The solution
You have entered
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2 2 8*x - 11*x*y + 6*y
$$6 y^{2} + \left(8 x^{2} - 11 x y\right)$$
8*x^2 - 11*x*y + 6*y^2
General simplification
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2 2 6*y + 8*x - 11*x*y
$$8 x^{2} - 11 x y + 6 y^{2}$$
6*y^2 + 8*x^2 - 11*x*y
The perfect square
Let's highlight the perfect square of the square three-member
$$6 y^{2} + \left(8 x^{2} - 11 x y\right)$$
Let us write down the identical expression
$$6 y^{2} + \left(8 x^{2} - 11 x y\right) = \frac{71 y^{2}}{32} + \left(8 x^{2} - 11 x y + \frac{121 y^{2}}{32}\right)$$
or
$$6 y^{2} + \left(8 x^{2} - 11 x y\right) = \frac{71 y^{2}}{32} + \left(2 \sqrt{2} x - \frac{11 \sqrt{2} y}{8}\right)^{2}$$
$$6 y^{2} + \left(8 x^{2} - 11 x y\right)$$
Let us write down the identical expression
$$6 y^{2} + \left(8 x^{2} - 11 x y\right) = \frac{71 y^{2}}{32} + \left(8 x^{2} - 11 x y + \frac{121 y^{2}}{32}\right)$$
or
$$6 y^{2} + \left(8 x^{2} - 11 x y\right) = \frac{71 y^{2}}{32} + \left(2 \sqrt{2} x - \frac{11 \sqrt{2} y}{8}\right)^{2}$$
Factorization
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/ / ____\\ / / ____\\ | y*\11 - I*\/ 71 /| | y*\11 + I*\/ 71 /| |x - -----------------|*|x - -----------------| \ 16 / \ 16 /
$$\left(x - \frac{y \left(11 - \sqrt{71} i\right)}{16}\right) \left(x - \frac{y \left(11 + \sqrt{71} i\right)}{16}\right)$$
(x - y*(11 - i*sqrt(71))/16)*(x - y*(11 + i*sqrt(71))/16)
Common denominator
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2 2 6*y + 8*x - 11*x*y
$$8 x^{2} - 11 x y + 6 y^{2}$$
6*y^2 + 8*x^2 - 11*x*y
Assemble expression
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2 2 6*y + 8*x - 11*x*y
$$8 x^{2} - 11 x y + 6 y^{2}$$
6*y^2 + 8*x^2 - 11*x*y
Combining rational expressions
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2 6*y + x*(-11*y + 8*x)
$$x \left(8 x - 11 y\right) + 6 y^{2}$$
6*y^2 + x*(-11*y + 8*x)
Rational denominator
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2 2 6*y + 8*x - 11*x*y
$$8 x^{2} - 11 x y + 6 y^{2}$$
6*y^2 + 8*x^2 - 11*x*y
Trigonometric part
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2 2 6*y + 8*x - 11*x*y
$$8 x^{2} - 11 x y + 6 y^{2}$$
6*y^2 + 8*x^2 - 11*x*y