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-y
( x-y ) 2
1
x 2 - y 2
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
0
{ -1,x[ 3;4 ) 1,x( 4;+ )
{ -1,x[ 3;4 ) 1,x[ 4;+ )
1
Question 4:   Factorise: x 3 -4 x 2 +8x-5
( x-1 )( x 2 -3x+5 )
( x-1 )( x 2 -2x+5 )
( x-1 )( x-2 )( x-3 )
( x-1 )( x 2 -3x+2 )
Question 5:   Simplify: 18 x 4 3 ÷ 12 x 7 3
2 x
4 x
x
2 x 3
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