Question

4(x+y)^2-x^2do by laying an identity
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Answer 1

Step-by-step explanation:

Aloha !

4(x+y)²-x²

4(x²+y²+2xy)-x²

=4x²+y²+8xy-x²

=3x²+y²+8xy

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@ Twilight Astro ☺️✌️❤️

Answer 2

Euler lived a century after Isaac Newton and Blaise Pascal, so he must have been familiar with the former's binomial theorem and the latter's triangle. Indeed, the polynomial you presented looks quite similar to the binomial expansion of (x−1)4, whose coefficients are found on the fourth row of Pascal's triangle. By subtracting the two, we are left with 4x2−8x−3, whose roots are 1±

√

7

2

which is a quarter of α. So,

P(x)=(x−1)4−4[(x−1)−

√

7

2

][(x−1)+

√

7

2

],

which, after substituting u=(x−1)2, becomes u2−4u+7. Then, by completing the square, we arrive at the desired result.