Question

2⁻² + (-3)⁻¹ = ?
2⁻² - (-3)⁻¹ = ?
2⁻² × (-3)⁻¹ = ?
2⁻² ÷ (-3)⁻¹ = ?

Dane sa wyrazenia 2x - 1 i 3 - x.Wyznacz i uprosc ich:
a) sume
b) roznice
c) iloczyn
d) podwojony iloczyn
e) roznicekwadratow
f) kwadrat roznicy

Answer 1

2⁻² + (-3)⁻¹ = 1/2^2 + 1/(-3)^1 = 1/4 - 1/3 = 3/12 - 4/12 = -1/12
2⁻² - (-3)⁻¹ = 1/2^2 - 1/(-3)^1 = 1/4 + 1-3 = 3/12 + 4/12 = 7/12
2⁻² ∙ (-3)⁻¹ = 1/2^2 ∙ 1/(-3)^1 = 1/4 ∙ (-1/3) = -1/12
2⁻² ÷ (-3)⁻¹ = 1/2^2 : 1/(-3)^1 = 1/4 : (-1/3) = 1/4 ∙ (-3/1) = -3/4

a) (2x - 1) + (3 - x) = 2x - 1 + 3 - x = x + 2
b) (2x - 1) - (3 - x) = 2x - 1 - 3 + x = 3x - 4
c) (2x - 1) ∙ (3 - x) = 6x - 2x^2 - 3 + x = -2x^2 + 7x - 3
d) [(2x - 1)(3 - x)] ∙ 2 = 2(6x - 2x^2 -3 + x) = 2(-2x^2 + 7x - 3) =
= -4x^2 + 14x - 6
e) (2x - 1)^2 - (3 - x)^2 = (4x^2 - 2x + z) - (9 - 6x + x^2) = 4x^2 -
- 2x + 1 - 9 + 6x - x^2 = 3x^2 + 4x + 8
f) [(2x-1) - (3-x)]^2 = (2x - 1)^2 - 2(2x-1)(3-x) + (3 - x)^2 = 4x^2 -
- 4x + 1 - [2(6x + 2x^2 - 3 + x)] + 9 - 6x + x^2 = 5x^2 - 10x + 10-
- (12x - 4x^2 - 6 + 2x) = 5x^2 - 10x + 10 - 12x + 4x^2 + 6 - 2x =
= 9x^2 - 24x + 16