因式分解下列各式。
１）p(xy-xz)+q(y-z)
２）(x-1)y+1-x
３）x(y-z)-y+z
４）(x-y)2次方+z(y-x)
５）x(ab-ac)+y(ac-ab)
６）(a+b)2次方-ax-bx
７）(x-y)2次方+2x+2y
８）x 2次方-1
９）64-49x 2次方
１０）(2-x)2次方-25x 2次方
１１）x 2次方+6x+9
１２）x 2次方+4xy+4y 2次方
１３）4(x-y)2次方+4a(x-y)+a 2次方
１４）x 2次方-3x+2
１５）x 2次方-5x+6
１６）x 2次方+2x-35
１７）x 2次方-6x-27
１８）x 2次方-5xy+6y 2次方
１９）
(a)因式分解 x 2次方-10x+25。
(b)利用(a)部結果，或其他方法，因式分解(x+1)2次方-10(x+1)+25。
２０）
(a)因式分解 x 2次方-4x+3。
(b)利用(a)部結果，或其他方法，因式分解(2x-3)2次方-4(2x-3)+3
中二數學問題(最快者有２０分)
2007-11-18 9:10 pm
回答 (2)
2007-11-18 9:39 pm
✔ 最佳答案
(1) p(xy-xz)+q(y-z)=px(y-z)+q(y-z)
=(px+q)(y-z)
(2) (x-1)y+1-x
=(x-1)y-(x-1)
=(x-1)(y-1)
(3) x(y-z)-y+z
=x(y-z)-(y-z)
=(x-1)(y-z)
(4) (x-y)²+z(y-x)
=(x-y)²-z(x-y)
=(x-y)[(x-y)-z]
=(x-y)(x-y-z)
(5) x(ab-ac)+y(ac-ab)
=x(ab-ac)-y(ab-ac)
=(x-y)(ab-ac)
=a(x-y)(b-c)
(6) (a+b)²-ax-bx
=(a+b)²-(a+b)x
=(a+b)(a+b-x)
(7) 無法分解
(8) x²-1
=x²-1²
=(x+1)(x-1)
(9) 64-49x²
=8²-(7x)²
=(8+7x)(8-7x)
(10) (2-x)²-25x²
=(2-x)²-(5x)²
=(2-x+5x)(2-x-5x)
=(2+4x)(2-6x)
(11) x²+6x+9
=(x+3)²
(12) x²+4xy+4y²
=(x+2y)²
(13) 4(x-y)²+4a(x-y)+a²
=[2(x-y)+a]²
=(2x-2y+a)²
(14) x²-3x+2
=(x-1)(x-2)
(15) x²-5x+6
=(x-2)(x-3)
(16) x²-2x+35
=(x+5)(x-7)
(17) x²-6x-27
=(x+3)(x-9)
(18) x²-5xy+6y²
=(x-2y)(x-3y)
(19)
(a) x²-10x+25
=(x-5)²
(b) (x+1)²-10(x+1)+25
=(x+1-5)²
=(x-4)²
(20)
(a) x²-4x+3
=(x-1)(x-3)
(b) (2x-3)²-4(2x-3)+3
=(2x-3-1)(2x-3-3)
=(2x-4)(2x-6)
=4(x-2)(x-3)
2007-11-19 12:44 am
(1) p(xy-xz)+q(y-z)
=px(y-z)+q(y-z)
=(px+q)(y-z)
(2) (x-1)y+1-x
=(x-1)y-(x-1)
=(x-1)(y-1)
(3) x(y-z)-y+z
=x(y-z)-(y-z)
=(x-1)(y-z)
(4) (x-y)²+z(y-x)
=(x-y)²-z(x-y)
=(x-y)[(x-y)-z]
=(x-y)(x-y-z)
(5) x(ab-ac)+y(ac-ab)
=x(ab-ac)-y(ab-ac)
=(x-y)(ab-ac)
=a(x-y)(b-c)
(6) (a+b)²-ax-bx
=(a+b)²-(a+b)x
=(a+b)(a+b-x)
(7) 無法分解
(8) x²-1
=x²-1²
=(x+1)(x-1)
(9) 64-49x²
=8²-(7x)²
=(8+7x)(8-7x)
(10) (2-x)²-25x²
=(2-x)²-(5x)²
=(2-x+5x)(2-x-5x)
=(2+4x)(2-6x)
(11) x²+6x+9
=(x+3)²
(12) x²+4xy+4y²
=(x+2y)²
(13) 4(x-y)²+4a(x-y)+a²
=[2(x-y)+a]²
=(2x-2y+a)²
(14) x²-3x+2
=(x-1)(x-2)
(15) x²-5x+6
=(x-2)(x-3)
(16) x²-2x+35
=(x+5)(x-7)
(17) x²-6x-27
=(x+3)(x-9)
(18) x²-5xy+6y²
=(x-2y)(x-3y)
(19)
(a) x²-10x+25
=(x-5)²
(b) (x+1)²-10(x+1)+25
=(x+1-5)²
=(x-4)²
(20)
(a) x²-4x+3
=(x-1)(x-3)
(b) (2x-3)²-4(2x-3)+3
=(2x-3-1)(2x-3-3)
=(2x-4)(2x-6)
=4(x-2)(x-3)
=px(y-z)+q(y-z)
=(px+q)(y-z)
(2) (x-1)y+1-x
=(x-1)y-(x-1)
=(x-1)(y-1)
(3) x(y-z)-y+z
=x(y-z)-(y-z)
=(x-1)(y-z)
(4) (x-y)²+z(y-x)
=(x-y)²-z(x-y)
=(x-y)[(x-y)-z]
=(x-y)(x-y-z)
(5) x(ab-ac)+y(ac-ab)
=x(ab-ac)-y(ab-ac)
=(x-y)(ab-ac)
=a(x-y)(b-c)
(6) (a+b)²-ax-bx
=(a+b)²-(a+b)x
=(a+b)(a+b-x)
(7) 無法分解
(8) x²-1
=x²-1²
=(x+1)(x-1)
(9) 64-49x²
=8²-(7x)²
=(8+7x)(8-7x)
(10) (2-x)²-25x²
=(2-x)²-(5x)²
=(2-x+5x)(2-x-5x)
=(2+4x)(2-6x)
(11) x²+6x+9
=(x+3)²
(12) x²+4xy+4y²
=(x+2y)²
(13) 4(x-y)²+4a(x-y)+a²
=[2(x-y)+a]²
=(2x-2y+a)²
(14) x²-3x+2
=(x-1)(x-2)
(15) x²-5x+6
=(x-2)(x-3)
(16) x²-2x+35
=(x+5)(x-7)
(17) x²-6x-27
=(x+3)(x-9)
(18) x²-5xy+6y²
=(x-2y)(x-3y)
(19)
(a) x²-10x+25
=(x-5)²
(b) (x+1)²-10(x+1)+25
=(x+1-5)²
=(x-4)²
(20)
(a) x²-4x+3
=(x-1)(x-3)
(b) (2x-3)²-4(2x-3)+3
=(2x-3-1)(2x-3-3)
=(2x-4)(2x-6)
=4(x-2)(x-3)
收錄日期: 2021-04-13 18:43:22
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071118000051KK01868