3. а) Упростите выражение: (х + 1)(х2 - x+1) - хх+3)(х – 3) б) Покажите, что значение выражения (х + 1)(х2 – x+1) - х(х+3)(х - 3) при х = 1 равно 10.
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a³ + b³ = (a + b)(a² - ab + b²)
a² - b² = (a - b)(a + b)
(х + 1)(х2 – x+1) - х(х+3)(х - 3) = x³ + 1³ - x(x² - 3²) = x³ + 1 - x³ + 9x = 9x + 1
при x = 1
9x +1 = 9*1 + 1 = 10