Question

Sorry za jakosc zdjecia ale myśle że da rade odczytac z góry dzięki za pomoc ;)
Zad.17

Answer 1

Ad.16
(3a - 1/2)² = 9a² - 3a + 1/4
(b + √3)² = b² + 2√3b + 3
(2c√2 - 3)² = 8c² - 12c√2 + 9

Ad. 17
a) 5x(2x - 3y) - (3x - 2y)² = 10x² - 15xy - (9x² -12xy + 4y²) = x² - 4y² - 3xy

b) (5x - 4y)(5x + 4y) - 1/4(10x - 2y)² = 25x² - 16y² - 1/4(100x² - 40xy + 4y²) =
25x² - 16y² - 25x² + 10xy - y² = -17y² + 10xy

c) (√2 + a)(a - √2) + (-3√2 + 2a)² = -2 + a² + (-18 - 12√2a + 4a²) = 5a² - 12√2a - 20

d) (2√2 + 4x)(4x - 2√2) - 2(2x - 1/4)² = -8 + 16x² - 2(4x² - 1x + 1/8) = -8 + 16x² - 8x² + 2x - 2/8 = 8x² + 2x -8,25

e) (1 - 2x)(1 + 2x) - (2y - x√2)² : 2 = 1 - 4x² - (4y² - 4√2xy + 2x²) : 2 = 1 - 4x² - 2y² + 2√2xy - x² = - 5x² - 2y² + 2√2xy + 1

f) (4x² + 1)(1/4x² + 9y²) - (x² + 3y)² = x^4 + 36x²y² + 1/4x² + 9y² - (x^4 + 6x²y + 9y²) = x^4 + 36x²y² + 1/4x² + 9y² - x^4 - 6x²y - 9y² =
36x²y² + 1/4x² - 6x²y

g) (-y - √7)² - (2x² - 7y)(7y - 2x²) = y² + 2√7y + 7 - (14x²y - 4x^4 - 49y² + 14 x²y) = y² + 2√7y + 7 - 14x²y + 4x^4 +49y² - 14 x²y = 4x^4 - 28x²y +50y² + 2√7y + 7

h) (xy² + 3x)(-xy² + 3x) - (3x)² = -x²y^4 + 3x²y² - 3x²y² + 9x² - 9x² = -x²y^4

[y^4 = y do potęgi 4]

Ad.18
(a +b)³ = a³ + 3a²b + 3ab² + b³
(a - b)³ = a³ - 3a²b + 3ab² - b³