First, multiple choice questions
1. The correct result of calculating (2a-3b) (2a+3b) is ().
a . 4a 2+9 B2 b . 4a 2-9 B2 c . 4a 2+ 12ab+9 B2
D.4a2- 12ab+9b2
2. If (x+a) (x+b) = x2-kx+ab, then the value of k is ().
a a+b B- a-b c a-b d b-a
3. The correct result of calculating (2x-3y) (4x2+6xy+9y2) is ().
A.(2x-3y)2b .(2x+3y)2c . 8x 3-27y 3d . 8x 3+27y 3
4. If the product of (x2-px+3) (x-q) does not contain the x2 term, then ()
A.p = QB.p = QC.p =-QD. Not sure.
5. If 0 < x < 1, then the value of algebraic expression (1-x) (2+x) is ().
A. it must be positive B. it must be negative C. it must be non-negative D. it cannot be determined.
6. The correct result of calculating (a2+2) (a4-2a2+4)+(a2-2) (a4+2a2+4) is ().
A.2(a2+2) B.2(a2-2) C.2a3 D.2a6
7. The solution of equation (x+4) (x-5) = x2-20 is ().
A.x=0 B.x=-4 C.x=5 D.x=40
8. If 2x2+5x+1= a (x+1) 2+b (x+1)+c, then a, b and c should be ().
A.a=2，b=-2，c=- 1
C.a=2，b= 1，c=-2 D.a=2，b=- 1，c=2
9. If 6x2-19x+15 = (ax+b) (CX+b), then AC+BD is equal to ().
a . 36 b . 15 c . 19d . 2 1
10. The product of (x+1) (x-1) and (x4+x2+ 1) is ().
a . X6+ 1 b . X6+2 x3+ 1 c . X6- 1d . X6-2 x3+ 1
Second, fill in the blanks
1.(3x- 1)(4x+5)=__________。
2.(-4x-y)(-5x+2y)=__________。
3.(x+3)(x+4)-(x- 1)(x-2)= _ _ _ _ _ _ _ _ _ _。
4.(y- 1)(y-2)(y-3)= _ _ _ _ _ _ _ _ _ _。
5. In the expansion formula of (x3+3x2+4x-1) (x2-2x+3), the coefficient of x4 is _ _ _ _ _ _ _.
6. If (x+a) (x+2) = x2-5x+b, then a = _ _ _ _ _ _ _ _ _ and b = _ _ _ _ _ _.
7. If A2+A+ 1 = 2, then (5-A) (6+A) = _ _ _ _ _.
8. When k = _ _ _ _ _ _ _ _ the product of polynomial x- 1 and 2-kx does not contain linear terms.
9. If the product of (x2+ax+8) (x2-3x+b) does not contain the terms x2 and x3, then a = _ _ _ _ _ _ _ _ _ _ _ _
10. If the base of the triangle is (3a+2b), the height is (9a2-6ab+4b2), and the area is _ _ _ _ _ _.
Third, answer questions.
1, calculate the following
( 1)(2x+3y)(3x-2y)(2)(x+2)(x+3)-(x+6)(x- 1)
(3)(3 x2+2x+ 1)(2 x2+3x- 1)(4)(3x+2y)(2x+3y)-(x-3y)(3x+4y)
2. Find the value of (a+b) 2-(a-b) 2-4ab, where a = 2002 and b = 200 1.
3,2 (2x-1) (2x+1)-5x (-x+3y)+4x (-4x2-52y), where x =- 1 and y = 2.
4. Solve the equation
(x- 1)(2y+ 1)= 2(x+ 1)(y- 1)x(2+y)-6 = y(x-4)
Fourth, explore a paradise for innovation.
1. If the coefficient of x3 is 5 and the coefficient of x2 is -6 in the product of (x2+ax-b) (2x2-3x+ 1),
Ask a, B.
2. According to (x+a) (x+b) = x2+(a+b) x+ab, directly calculate the following questions.
( 1)(x-4)(x-9)(2)(xy-8a)(xy+2a)
Five, mathematics life practice
A piece of glass with a length of am and a width of bm can cover a desk top just after the length and width are cut off by cm (the glass is the same size as the top). What is the countertop area?
Six, thinking about the problem:
Please calculate: if 1+X+X2+X3 = 0, find the value of X+X2+X3+…+X2000.