Question

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Oblicz i uprośc :
a) -(x# -4x-4)+(-2+x+3x#)=
b) (x-2)(x#-3x-1)=
c) (2a-b)(3a+4b)-2(a+3b)(b-2a)=
d)-4(4a-3b)(a-b)+3(a+2b)(b-3a)=
e)[4(x#-3x+2)-3(2-5x+3x#)](4x+5)=

Answer 1

A)

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

= 2x² + 5x + 2

b)

(x - 2)(x² - 3x - 1) = x³ - 3x² - x - 2x² + 6x + 2 = x³ - 5x² + 5x + 2

c)

(2a-b)(3a+4b) - 2(a+3b)(b-2a) = 6a² + 8ab - 3ab - 4b² - 2(ab - 2a² +3b² - 6ab) =

= 6a² + 5ab - 4b² - 2(- 2a² + 3b² - 5ab) =

= 6a² + 5ab - 4b² + 4a² + 5ab - 6b² =

= 10a² + 10ab - 10b²

d)

-4(4a-3b)(a-b)+3(a+2b)(b-3a) = - 4(4a² - 4ab - 3ab + 3b²) +3(ab - 3a²+2b²-6ab)=

= - 16a² +28ab - 12b² - 9a² - 15ab +6b² =

= - 25a² + 13ab - 6b²

e)

[4(x² - 3x + 2)-3(2 - 5x + 3x²)](4x + 5) = (4x² - 12x + 8 - 6 + 15x - 9x²)(4x + 5)=

= (- 5x² + 3x + 2)(4x+5) =

= - 20x³ - 25x² + 12x² + 15x + 8x + 10 =

= - 20x³ - 13x² + 23x + 10

Answer 2

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

(x-2)(x²-3x-1)= x³ - 3x² - x - 2x² + 6x +2 = x³ - 5x² +5x +2

(2a-b)(3a+4b)-2(a+3b)(b-2a)=6a²+ 8ab-3ab-4b² -2(ab2a²+3b²-6ab)=
=6a² + 8ab - 3b - 4b² - 2ab +4a² -6b² +12ab =
=12a² +18ab -3b -10b²

-4(4a-3b)(a-b)+3(a+2b)(b-3a)=
=-4(4a²- 4ab- 3ab + 3b²) +3(ab - 3a² +2b² -6ab)=
=-16a² +16ab +12ab -12b² +3ab - 9a² +6b² -6ab) =
=-25a² +25ab -6b²

[4(x²-3x+2)-3(2-5x+3x²)](4x+5)=
=(4x²-12x+5 +15x -9x²)(4x+5)=
=16x³ +20x² - 48x²- 60x +20x +25 +50x² +65x -36x² -45x² =
=16x³ -58x² +25x +25