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2.1 Exercises

From Förberedande kurs i matematik 1

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Exercise 2.1:1

Expand

a) 3x(x−1) b) (1+x−x2)xy c) −x2(4−y2)
d) x3y2y1−1xy+1  e) (x−7)2 f) (5+4y)2
g) (y2−3x3)2 h) (5x3+3x5)2

Svar | Lösning a | Lösning b | Lösning c | Lösning d | Lösning e | Lösning f | Lösning g | Lösning h


Exercise 2.1:2

Expand

a) (x−4)(x−5)−3x(2x−3) b) (1−5x)(1+15x)−3(2−5x)(2+5x)
c) (3x+4)2−(3x−2)(3x−8) d) (3x2+2)(3x2−2)(9x4+4)
e) (a+b)2+(a−b)2

Svar | Lösning a | Lösning b | Lösning c | Lösning d | Lösning e

Exercise 2.1:3

Factorise and simplify as much as possible

a) x2−36 b) 5x2−20 c) x2+6x+9
d) x2−10x+25 e) 18x−2x3 f) 16x2+8x+1

Svar | Lösning a | Lösning b | Lösning c | Lösning d | Lösning e | Lösning f

Exercise 2.1:4

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

a) (x+2)(3x2−x+5)
b) (1+x+x2+x3)(2−x+x2+x4)
c) (x−x3+x5)(1+3x+5x2)(2−7x2−x4)

Svar | Lösning a | Lösning b | Lösning c

Exercise 2.1:5

Simplify as much as possible

a) 1x−x2−x1 b) 1y2−2y−2y2−4
c) (x+1)(x+2)(3x2−12)(x2−1) d) (y2+4)(y2−4)(y2+4y+4)(2y−4)

Svar | Lösning a | Lösning b | Lösning c | Lösning d

Exercise 2.1:6

Simplify as much as possible

a) x−y+x2y−x  y2x−y−1  b) xx−2+xx+3−2
c) 2a+ba2−ab−2a−b d) \displaystyle \displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}

Svar | Lösning a | Lösning b | Lösning c | Lösning d

Exercise 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}

Svar | Lösning a | Lösning b | Lösning c

Exercise 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}}}

Svar | Lösning a | Lösning b | Lösning c

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