F.2數學題目21條[急急急急]

1. sim (-2x{3}+6x-3)+(4x{3}-6x+2)
= -2x^3+6x-3+4x^3-6x+2
= 2x^3+1

2. sim (b{4}-7b{2}+1)-(3b{4}-2b{2}-6)
=b^4-7b^2+1-3b^4-2b^2-6
= -2b^4-9b^2-5
= -(2b^4+9b^2+5)

3. sim (5a{3}-a{2})+(6a{2}-7a+1)-(2a{3}+4a-1)
=5a^3-a^2+6a^2-7a+1-2a^3-4a+1
=3a^3+5a^2-11a+2

4. ex (2a+1)(a-2)
=2a^2+a-2a-2
=2a^2+a-2

5. ex (3b{2}-2b+1)(b-1)
=3b^3-2b^2+b-3b^2+2b-1
=3b^3-5b^2+3b-1

6. ex (2x{2}-3x+1)(x{2}-x-1)
=2x^4-3x^3+x^2-2x^3+3x^2-x-2x^2+3x-1
=2x^4-5x63+2x^2+2x-1

7. fact 2a{2}b-4ab{2}
=2(a^2b-2ab^2)
=2ab(a-2b)

8. fact -3xy{2}z+6x{2}yz{2}-9xy{2}z{2}
=3xyz(-y+2xz-3yz)

9. fact x(a-b)+y(b-a)
=x(a-b)-y[-(b-a)]
=x(a-b)-y(a-b)
=(x-y) (a-b)

10. fact (x-y){3}- (x-y){2}
=(x-y)^2(x-y)-1(x-y)
=(x-y)2(x-y-1)

11. fact (2a-b)(x+y)+(b-2a)(x+y)
=(x+y)(2a-b+b-2a)
=(x+y)(0)
=0

12. fact ax-bx+cx+cy-by+ay
=x(a-b+c)+y(a-b+c)
=(x+y) (a-b+c)

13. fact xy+x+y+1
=x(y+1)+(y+1)
=(x+1)(y+1)

14. fact x{2}-25
=x^2-(5)^2
=(x+5)(x-5)

15.fact 16a{2}-81b{2}
=(4a)^2-(9b)^2
=(4a+9b)(4a-9b)

16. fact (x+y){2}-9
=(x+y)^2-3^2
=(x+y-3) (x+y+3)

17. fact (a+b){2}-(c+d){2}
=[a+b-(c+d)] [a+b+(c+d)]
=(a+b-c-d) (a+b+c+d)

18. fact (9x{2}+6xy+y{2}
=(3x)^2+2(3x)(y)+y^2
=(3x+y) (3x+y)
=(3x+y)^2

19. fact 4x{2}- 12xy+9y{2}
=(2x)^2-2(4x)(3y)+(3y)^2
=(2x-3y) (2x-3y)
=(2x-3y)^2

20. fact a{2}-b{2}+ax-bx
=(a-b)(a+b)+x(a-b)
=(a-b)(a+b+x)

21. p{4}-2p{2}q{2}+q[4]
=(p^2)^2-2(p)^2(q)^2+(q^2)^2
=(p^2-q^2) (p^2-q^2)
=(p-q) (p+q) (p-q) (p+q)
=[(p-q) (p+q)]^2

1. (-2x3+6x-3)+(4x3-6x+2)
=2x3-1
2. (b4-7b2+1)-(3b4-2b2-6)
=-2b4-5b2+7
3. (5a3-a2)+(6a2-7a+1)-(2a3+4a-1)
=3a3+5a2-11a+2
4. (2a+1)(a-2)
=2a2-4a+a-2
=2a2-3a-2

5. (3b2-2b+1)(b-1)
=3a3-2b2+b-3b2+2b-1
=3a3-5b2+3b-1
6. (2x2-3x+1)(x2-x-1)
=2x4-3x3+x2-2x3+3x2-x-2x2+3x-1
=2x4-5x3+2x2+2x-1
7. 2a2b-4ab2
=2ab(a-2b)
8. -3xy2z+6x2yz2-9xy2z2
=-3xy(y-2xz+3yz)
9. x(a-b)+y(b-a)
=x(a-b)-y(a-b)
=(a-b)(x-y)
10. (x-y)3- (x-y)2
=(x-y)2(x-y-1)
11. (2a-b)(x+y)+(b-2a)(x+y)
=(x+y)[(2a-b)+(b-2a)]
=(x+y)(0)
=0
12. ax-bx+cx+cy-by+ay
=x(a-b+c)+y(a-b+c)
=(x+y)(a-b+c)

13. xy+x+y+1
=x(y+1)+(y+1)
=(y+1)(x+1)
14. x2-25
=(x-5)(x+5)

15.16a2-81b2
=(4a-9b)(4a+9b)

16. (x+y)2-9
=(x+y-3)(x+y+3)
17. (a+b)2-(c+d)2
=[(a+b)-(c+d)][(a+b)+(c+d)]
=(a+b-c-d)(a+b+c+d)

18. 9x2+6xy+y2
=(3x+y)2


19. 4x2- 12xy+9y2
(2x-3y)2

20. a2-b2+ax-bx
=(a-b)(c+b)+x(a-b)
=(a-b)(c+b+x)

21. p4-2p2q2+q4
=(p2-q2)2