Question

write down all identities of a polynomial.​

Answer 1

$\sf1) \\ \sf( x + y ){}^{2} = x² + 2xy +y²$

$\sf \: 2) \\ \sf( x \: – \: y) 2 = x {}^{2} – 2xy + y {}^{2}$

$\sf \: 3) \\ \sf(x + y)(x – y) = x {}^{2} – y {}^{2}$

$\sf 4) \\ \sf(x + a)(x + b) = x {}^{2} +(a + b)x + ab$

$\sf 5) \\ \sf(x + y) 3 = x³ + 3x²y + 3xy² + y³ = x³ + y³ +3xy(x +y)$

$\sf 6) \\ \sf(x - y) 3 = x3 - 3x²y + 3xy² - y³ = x³+ y³ -3xy(x –y)$

$\sf 7) \\ \sf(x + y + z) 2 = x² + y² + z² + 2xy + 2yz + 2zx$

$\sf 8) \\ \sf \: x³ + y³ = (x + y)(x² – xy + y²)$

$\sf 9) \\ \sf \: x³ - y³ = (x - y)(x² + xy + y²)$

$\sf 10) \\ \sf \: x³ + y³ + z³ – 3xyz = (x + y + z)(x² + y² + z² – xy – yz – zx)$