ALGECON PRACTICE EXERCISES 1
I. Perform the indicated operations
2 2 2 2
1. Add 2x + xy−5 y and −7 x −5 xy−6 y
2. Subtract 2a + 2b – 4c from the sum of 4a – 7b + 12c and 5b – 3c
3. (25)(2-7)(2-2)
4.
−2 2
u3 v−1 w−2
5.
[( u−2 v −2 w
2
)]
2
6. 3 xy(2x+3 x y)−2 x y(4−xy )
2n n
7. (2 x −x +10)( x−1 )
3
8. Divide 4 x −2 x+3 by 2x – 1
9. Divide 16a4n - 64a10n by 2a3n
4 2 2
10. Divide 3 x −4 x +8 x+3 by 3 x +6 x+2
II. Use special product formulas to find the following.
1. ( 7x + 3y ) ( 2x – 4y)
2. ( 2mn – 3r) ( 5mn + 2r )
2
3. ( 5 x−3 y)
2
4. ( 5 x− y+2z )
3
5. ( 4 x−y)
6. [(3 x−2 y ) +4 z ] [(3x−2 y ) −4 z]
2 2
7. [(2 x −x)−3] [(2 x −x)+3]
8. ( 4x - 3y) ( 4x + 3y)
2 3 2 3
9. [(2x −x) +( x −1)] [(2x −x) −( x −1)]
ab c ab c
10.
( 3
+4 ) ( 3
−4 )
III. Factor the following completely.
3 2
1. 2 x +4 x −10 x
2. 6 xy 2 z3 −12 x 2 yz 2 +4 xy 3 z 2
2 2
3. 3 x ( x+3 y )+6 xz(x+3 y )
4. 4 x 4− y 8 z6
2 4
5. 81(2x +3 z) −4 r
6. a2 b2 −ab−20
2
7. 10 x +11 x−6
6 5 4
8. 16 x +24 x +9 x
2
9. a −ab ++ a−b
4 2 2
10. x + 2 x +1−x
I. Perform the indicated operations
2 2 2 2
1. Add 2x + xy−5 y and −7 x −5 xy−6 y
2. Subtract 2a + 2b – 4c from the sum of 4a – 7b + 12c and 5b – 3c
3. (25)(2-7)(2-2)
4.
−2 2
u3 v−1 w−2
5.
[( u−2 v −2 w
2
)]
2
6. 3 xy(2x+3 x y)−2 x y(4−xy )
2n n
7. (2 x −x +10)( x−1 )
3
8. Divide 4 x −2 x+3 by 2x – 1
9. Divide 16a4n - 64a10n by 2a3n
4 2 2
10. Divide 3 x −4 x +8 x+3 by 3 x +6 x+2
II. Use special product formulas to find the following.
1. ( 7x + 3y ) ( 2x – 4y)
2. ( 2mn – 3r) ( 5mn + 2r )
2
3. ( 5 x−3 y)
2
4. ( 5 x− y+2z )
3
5. ( 4 x−y)
6. [(3 x−2 y ) +4 z ] [(3x−2 y ) −4 z]
2 2
7. [(2 x −x)−3] [(2 x −x)+3]
8. ( 4x - 3y) ( 4x + 3y)
2 3 2 3
9. [(2x −x) +( x −1)] [(2x −x) −( x −1)]
ab c ab c
10.
( 3
+4 ) ( 3
−4 )
III. Factor the following completely.
3 2
1. 2 x +4 x −10 x
2. 6 xy 2 z3 −12 x 2 yz 2 +4 xy 3 z 2
2 2
3. 3 x ( x+3 y )+6 xz(x+3 y )
4. 4 x 4− y 8 z6
2 4
5. 81(2x +3 z) −4 r
6. a2 b2 −ab−20
2
7. 10 x +11 x−6
6 5 4
8. 16 x +24 x +9 x
2
9. a −ab ++ a−b
4 2 2
10. x + 2 x +1−x
