ZADANIE NR 14 A) 3(x² + 2x - 1) + 5x(2x² - 6x - 3) = 3x² + 6x - 3 + 10x³ - 30x² - 15x = = 10x³ - 27x² - 9x - 3 B) 4x²(x + 6) - 12x(x² + 9x - 1) = 4x³ + 24x² - 12x³ - 108x² + 12x = = - 8x³ - 84x² + 12x = - 4x(2x² + 21x - 3) C) 7x²(8x - 1) - 7x²(8x + 1) = 7x²[(8x - 1) - (8x + 1)] = = 7x²(8x - 1 - 8x - 1) = 7x² * (- 2) = - 14x² D) x²(x² - 3x + 1) - x³(4x + 9) = x^4 - 3x³ + x² - 4x^4 - 9x³ = = - 3x^4 - 12x³ + x² = - x²(3x² + 12x - 1) E) x³(x² - 1) - x²(x³ - 1) = x^5 - x³ - x^5 + x² = - x³ + x² = -x²(x - 1) F) - 2x(- 1/8x + 1/12) - 1/4x²(8x - 4) = 1/4x² - 1/6x - 2x³ + x² = = - 2x³ + 5/4x² - 1/6x = - 1/12x(24x² - 15x + 2)
ZADANIE 14 a) 3(x² + 2x - 1) + 5x(2x² - 6x - 3) = 3x² + 6x - 3 + 10x³ - 30x² - 15x = = 10x³ - 27x² - 9x - 3 b) 4x²(x + 6) - 12x(x² + 9x - 1) = 4x³ + 24x² - 12x³ - 108x² + 12x = = - 8x³ - 84x² + 12x = - 4x(2x² + 21x - 3) c) 7x²(8x - 1) - 7x²(8x + 1) = 7x²[(8x - 1) - (8x + 1)] = = 7x²(8x - 1 - 8x - 1) = 7x² * (- 2) = - 14x² d) x²(x² - 3x + 1) - x³(4x + 9) = x^4 - 3x³ + x² - 4x^4 - 9x³ = = - 3x^4 - 12x³ + x² = - x²(3x² + 12x - 1) e) x³(x² - 1) - x²(x³ - 1) = x^5 - x³ - x^5 + x² = - x³ + x² = -x²(x - 1) f) - 2x(- 1/8x + 1/12) - 1/4x²(8x - 4) = 1/4x² - 1/6x - 2x³ + x² = = - 2x³ + 5/4x² - 1/6x = - 1/12x(24x² - 15x + 2)