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2.1 Exercises

From Förberedande kurs i matematik 1

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Revision as of 10:38, 10 September 2008

       Theory          Exercises      


Exercise 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


Exercise 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

Exercise 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

Exercise 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)

Exercise 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)

Exercise 2.1:6

Simplify as much as possible

a) xy+x2yx  y2xy1  b) xx2+xx+32
c) 2a+ba2ab2ab d) ab+b2a+b1a+bab2

Exercise 2.1:7

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

a) 2x+32x+5 b) x+1x1+1x2 c) axa+1ax2(a+1)2

Exercise 2.1:8

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

a)  3+x  xx+1  b) 1x3x3x1 c) 11+11+11+x