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2.1 Übungen

Aus Online Mathematik Brückenkurs 1

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Version vom 09:41, 22. Okt. 2008

       Theorie          Übungen      


Übung 2.1:1

Expand

a) 3x(x1) b) (1+xx2)xy c) x2(4y2)
d) x3y2y11xy+1  e) (x7)2 f) (5+4y)2
g) (y23x3)2 h) (5x3+3x5)2


Übung 2.1:2

Expand

a) (x4)(x5)3x(2x3) b) (15x)(1+15x)3(25x)(2+5x)
c) (3x+4)2(3x2)(3x8) d) (3x2+2)(3x22)(9x4+4)
e) (a+b)2+(ab)2

Übung 2.1:3

Factorise and simplify as much as possible

a) x236 b) 5x220 c) x2+6x+9
d) x210x+25 e) 18x2x3 f) 16x2+8x+1

Übung 2.1:4

Determine the coefficients in front of x and x2  when the following expressions are expanded out.

a) (x+2)(3x2x+5)
b) (1+x+x2+x3)(2x+x2+x4)
c) (xx3+x5)(1+3x+5x2)(27x2x4)

Übung 2.1:5

Simplify as much as possible

a) 1xx2x1 b) 1y22y2y24
c) (x+1)(x+2)(3x212)(x21) d) (y2+4)(y24)(y2+4y+4)(2y4)

Übung 2.1:6

Simplify as much as possible

a) xy+x2yx  y2xy1  b) xx2+xx+32
c) 2a+ba2ab2ab d) \displaystyle \displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}

Übung 2.1:7

Simplify the following fractions by writing them as an expression having a common fraction sign

a) \displaystyle \displaystyle \frac{2}{x+3}-\frac{2}{x+5} b) \displaystyle x+\displaystyle \frac{1}{x-1}+\displaystyle \frac{1}{x^2} c) \displaystyle \displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}

Übung 2.1:8

Simplify the following fractions by writing them as an expression having a common fraction sign

a) \displaystyle \displaystyle \frac{\displaystyle\ \frac{x}{x+1}\ }{\ 3+x\ } b) \displaystyle \displaystyle \frac{\displaystyle \frac{3}{x}-\displaystyle \frac{1}{x}}{\displaystyle \frac{1}{x-3}} c) \displaystyle \displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}