標題:
F.2數學題目21條[急急急急]
發問:
要step....Simplify=simExpand= exFactorize=fact在{}既數字係幾多次方1. sim (-2x{3}+6x-3)+(4x{3}-6x+2)2. sim (b{4}-7b{2}+1)-(3b{4}-2b{2}-6)3. sim (5a{3}-a{2})+(6a{2}-7a+1)-(2a{3}+4a-1)4. ex (2a+1)(a-2)5. ex (3b{2}-2b+1)(b-1)6. ex (2x{2}-3x+1)(x{2}-x-1)7. fact 2a{2}b-4ab{2}8. fact ... 顯示更多 要step.... Simplify=sim Expand= ex Factorize=fact 在{}既數字係幾多次方 1. sim (-2x{3}+6x-3)+(4x{3}-6x+2) 2. sim (b{4}-7b{2}+1)-(3b{4}-2b{2}-6) 3. sim (5a{3}-a{2})+(6a{2}-7a+1)-(2a{3}+4a-1) 4. ex (2a+1)(a-2) 5. ex (3b{2}-2b+1)(b-1) 6. ex (2x{2}-3x+1)(x{2}-x-1) 7. fact 2a{2}b-4ab{2} 8. fact -3xy{2}z+6x{2}yz{2}-9xy{2}z{2} 9. fact x(a-b)+y(b-a) 10. fact (x-y){3}- (x-y){2} 11. fact (2a-b)(x+y)+(b-2a)(x+y) 12. fact ax-bx+cx+cy-by+ay 13. fact xy+x+y+1 14. fact x{2}-25 15.fact 16a{2}-81b{2} 16. fact (x+y){2}-9 17. fact (a+b){2}-(c+d){2} 18. fact (9x{2}+6xy+y{2} 19. fact 4x{2}- 12xy+9y{2} 20. fact a{2}-b{2}+ax-bx 21. p{4}-2p{2]q{2}+q[4}
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最佳解答:
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
其他解答:
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
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