Test: Algebraic expressions I - Ambitious

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Question 1:   Expand and simplify: 4x y 3 ( xy-5 y 2 )=...
4 x 2 y 4 -20x y 5
4 x 2 y 4 -20x y 4
4 x 2 y 2 -20x y 5
4 x 2 y 4 -5x y 5
Question 2:   Expand and simplify: ( x 2 -6)(2x-7)=...
2 x 3 -7 x 2 +42
2 x 3 -7x-12x+42
2 x 3 -19 x 2 +42
2 x 3 -7 x 2 -12x+42
Question 3:   Simplify: 9 x 2 - y 2 3x+y ( 3x-y )=...
3x+y
3x-y
1
9 x 2 -6xy+ y 2
Question 4:   Find remainder of division x 3 -4 x 2 +x+7 by x-1
0
4
1
5
Question 5:   Find remainder of division x 3 +6 x 2 +x-4 by x+1
2
1
0
5
Question 6:   Factorise: -6 x 3 + x 2 +6x-1
( 6x-1 )( 1-x )( 1+x )
( 6x-1 )( 6x+1 )( 1-x )
( 6x-1 ) ( 1-x ) 2
( 6x-1 )( 1- x 2 )
Question 7:   Factorise x 4 -2 x 2 +1
( x-1 ) 2
( x 2 -1 ) 2
( x-1 )( x+1 )
( x-1 ) 2 ( x+1 ) 2
Question 8:   Simplify: ( x-4 )( x 2 -5x+4 ) x 2 -8x+16
x-1 x-4
1
x-4
x-1
Question 9:   Simplify: 16( x 3 -1 ) 12( x 2 +x+1 )
16 12 ( x-1 )
4 3 ( x 2 +x+1 )
4 3 ( x 3 -1 )
4 3 ( x-1 )
Question 10:   Simplify: ( x-y ) 2 3 ÷ ( x-y ) 1 6
1
( x-y ) 1 2
( x-y ) 2
( x-y ) 1 6