Odpowiedź:
zad 3.12
a)
3(2 - x)² + 2(x - 3)(x + 3) - (2x - 3)² =
= 3(4 - 4x + x²) + 2(x² - 9) - (4x² - 12x + 9) =
= 12 - 12x + 3x² + 2x² - 18 - 4x² + 12x - 9 = x² - 15
b)
2(2x - 3)(2x + 3) - 3(x + 5)² + 1/2(2x - 1)² + 32(x + 1/2) =
= 2(4x² - 9) - 3(x² + 10x + 25) + 1/2(4x² - 4x + 1) + 32x + 16 =
= 8x² - 18 - 3x² - 30x - 75 + 2x² - 2x + 1/2 + 32x + 16 =
= 7x² - 81
c)
15 - 4(x - 1)(x + 1) + (3x - 2)² - (x + 2)² - 4(x - 3/2)² =
= 15 - 4(x² - 1) + 9x² - 12x + 4 - x² - 4x - 4 - 4(x² - 3x + 9/4) =
= 15 - 4x² + 4 + 9x² - 12x + 4 - x² - 4x - 4 - 4x² + 12x - 9 =
= - 4x + 10
d)
(5 - x)² + 3(x - 2)(2 + x) - 4(x - 2 1/2)² - 10(x - 1) =
= 25 - 10x + x² + 3(x² - 4) - 4(x² - 25x + 25/4) - 10x + 1 =
= 25 - 10x + x² + 3x² - 12 - 4x² + 100x - 25 - 10x + 1 =
= 80x - 11
