Test: Algebraic expressions I - Challenging

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Question 1:   Simplify: ( x + y ) 2 + ( x - y ) 2 2( x 2 - y 2 ) ÷ 1 x 3 - y 3 -3xy
x 2 - y 2
x-y
( x-y ) 2
1
Question 2:   Divide x 4 -7 x 3 +5 x 2 +6x-7 by x+1
x 3 -8 x 2 +13x-5
x 3 -8 x 2 +10x-7
x 3 -8 x 2 +13x-7
x 3 -8 x 2 -7
Question 3:   Simplify: x-2-2 x-3 x-3 -1
{ -1,x[ 3;4 ) 1,x[ 4;+ )
0
{ -1,x[ 3;4 ) 1,x( 4;+ )
1
Question 4:   Factorise: x 3 -4 x 2 +8x-5
( x-1 )( x 2 -3x+2 )
( x-1 )( x-2 )( x-3 )
( x-1 )( x 2 -2x+5 )
( x-1 )( x 2 -3x+5 )
Question 5:   Simplify: 18 x 4 3 ÷ 12 x 7 3
2 x 3
x
4 x
2 x
Question 6:   Simplify: a 1 + a 2 ++ a 1000 a -1 + a -2 ++ a -1000
1 a 1000
1 a 1001
a 1001
a 1000
Question 7:   Factorise: x 3 -3x+2
( x-1 )( x 2 +x-2 )
( x-1 ) 2 ( x+2 )
( x-1 )( x+2 )
( x-1 ) ( x+2 ) 2
Question 8:   Simplify: x 7 + x 14 x -7 + x -14
1 x 21
x 20
x 21
1 x 7
Question 9:   Simplify: 1 ( x+3 ) 2 ( 1 x 2 + 1 9 )+ 2 ( x+3 ) 3 ( 1 x + 1 3 )
1 3x
1 9x
1 9 x 2
9 x 2
Question 10:   Reduce: ( x-2 ) 2 ( x 2 -9 ) ( x 3 -27 )( x 2 -4 )
x-2 x+2
x-3 x 2 +3x+9
( x-2 )( x+3 ) ( x+2 )( x 2 +3x+9 )
x-2 ( x-3 ) 2