Question

8. Descompuneţi în factori: a) (x + 4)²-9; d) 25x² - (x - 1)²; b) 16-(x - 2)²; e) 9(x + 2)² - 16; c) (3x + 2)² - 4x²; f) (x + 2)² - (2x - 1)².​

Answer 1

Răspuns:

a) (x + 4)² - 9 = (x + 4)(x + 4) - 3(3) = (x + 4)² - 3² = (x + 4 + 3)(x + 4 - 3) = (x + 7)(x + 1)

d) 25x² - (x - 1)² = 25x² - (x - 1)(x - 1) = 25x² - (x² - 2x + 1) = (25 - 1)x² + 2x - 1 = 24x² + 2x - 1

b) 16 - (x - 2)² = 16 - (x - 2)(x - 2) = 16 - (x² - 4x + 4) = 16 - x² + 4x - 4 = -x² + 4x + 12

e) 9(x + 2)² - 16 = 9(x + 2)(x + 2) - 4(4) = 9(x + 2)² - 4² = 9(x + 2 + 2)(x + 2 - 2) = 9(x + 4)(x)

c) (3x + 2)² - 4x² = (3x + 2)(3x + 2) - 4x(2x) = (3x + 2)² - 4x² = (3x + 2 + 2x)(3x + 2 - 2x) = (5x + 2)(x + 2)

f) (x + 2)² - (2x - 1)² = (x + 2)(x + 2) - (2x - 1)(2x - 1) = (x + 2)² - (2x - 1)² = (x + 2 + 2x - 1)(x + 2 - 2x + 1) = (3x + 1)(x + 3)

Sper ca te-am ajutat :)