Factorize the following expression:
1) (2x-y)^2 -x^2
2) (2x+y)^2 - (x+2y)^2
3) 4(2x+y)^2+4(2x+y)+1
F.2 math factorize quick,,plz help
2007-10-24 5:59 am
回答 (7)
2007-10-24 6:20 am
✔ 最佳答案
1) (2x-y)^2 -x^2=4x^2-4xy+y^2-x^2
=3x^2-4xy+y^2
=(x-y)(3x-y)
2) (2x+y)^2 - (x+2y)^2
=4x^2+4xy+y^2-x^2-4xy-4y^2
=3x^2-3y^2
=3(x+y)(x-y)
3)1st way:
4(2x+y)^2+4(2x+y)+1
=[2(2x+y)+1]^2
=(4x+2y+1)^2
2nd way:
let (2x+y) be A
4(2x+y)^2+4(2x+y)+1
=4A^2+4A+1
=(2A+1)^2
=[2(2x+y)+1]^2
=(4x+2y+1)^2
As you see, in Q3, the 1st way and the 2nd way are actually the same. But if you cannot really understand what's going on in the 1st way, the 2nd way is easier to understand.
Hope I can help you.
參考: me
2007-10-24 6:23 am
1)2(2x-y)^2-X^2
=(2x-y)(2x-y)-x^2
=(2x-y)(2x-y-x^2)
2)(2X+y)^2-(x+2y)^2
=(2x+y)(2x+y)-(x+2y)(x+2y)
=(2x+y)(x+2y-1)
3)4(2x+y)^2+4(2x+y)+1
=4(2x+1)(2x+y)+4(2x+y)+1
=(2x+y)(2x+y)[4(2x+y)+1]
=(2x+y)(8x+4y+1)
=(2x-y)(2x-y)-x^2
=(2x-y)(2x-y-x^2)
2)(2X+y)^2-(x+2y)^2
=(2x+y)(2x+y)-(x+2y)(x+2y)
=(2x+y)(x+2y-1)
3)4(2x+y)^2+4(2x+y)+1
=4(2x+1)(2x+y)+4(2x+y)+1
=(2x+y)(2x+y)[4(2x+y)+1]
=(2x+y)(8x+4y+1)
參考: 第2題唔係太識
2007-10-24 6:14 am
1) (2x-y)^2 -x^2
= (2x-y+x)(2x-y-x)
= (3x-y(x-y)
2) (2x+y)^2 - (x+2y)^2
= (2x+y+x+2y)(2x+y-x-2y)
= (3x+3y)(x-y)
= 3(x+y)(x-y)
3) 4(2x+y)^2+4(2x+y)+1
=[2(2x+y)]^2 + 2[2(2x+y)] + 1^2
=[2(2x+y)+1]^2
=(4x+2y+1)^2
個個答案都一樣
= (2x-y+x)(2x-y-x)
= (3x-y(x-y)
2) (2x+y)^2 - (x+2y)^2
= (2x+y+x+2y)(2x+y-x-2y)
= (3x+3y)(x-y)
= 3(x+y)(x-y)
3) 4(2x+y)^2+4(2x+y)+1
=[2(2x+y)]^2 + 2[2(2x+y)] + 1^2
=[2(2x+y)+1]^2
=(4x+2y+1)^2
個個答案都一樣
2007-10-24 6:06 am
1)
(2x-y)^2 -x^2
= [(2x-y)+x] [(2x-y)-x]
= (2x-y+x)(2x-y-x)
= (3x-y)(x-y)
2)
(2x+y)^2 - (x+2y)^2
= [(2x+y)+(x+2y)][(2x+y)-(x+2y)]
= (2x+y+x+2y)(2x+y-x-2y)
= (3x+3y)(x-y)
= 3(x+y)(x-y)
3)
4(2x+y)^2+4(2x+y)+1
= [2(2x+y)+1]^2
= (4x+2y+1)^2
有錯請指正!
(2x-y)^2 -x^2
= [(2x-y)+x] [(2x-y)-x]
= (2x-y+x)(2x-y-x)
= (3x-y)(x-y)
2)
(2x+y)^2 - (x+2y)^2
= [(2x+y)+(x+2y)][(2x+y)-(x+2y)]
= (2x+y+x+2y)(2x+y-x-2y)
= (3x+3y)(x-y)
= 3(x+y)(x-y)
3)
4(2x+y)^2+4(2x+y)+1
= [2(2x+y)+1]^2
= (4x+2y+1)^2
有錯請指正!
參考: My Maths knowledge
2007-10-24 6:05 am
1) (2x-y)^2 -x^2
= (2x - y + x)(2x - y - x)
= (3x - y)(x - y)
2) (2x+y)^2 - (x+2y)^2
= (2x + y + (x + 2y))(2x + y - (x + 2y))
= (3x + 3y)(x - y)
= 3(x + y)(x - y)
3) 4(2x+y)^2+4(2x+y)+1
= [2(2x + y)]^2 + 2[2(2x + y)][1] + 1^2
= [2(2x + y) + 1]^2
= (4x + 2y + 1)^2
= (2x - y + x)(2x - y - x)
= (3x - y)(x - y)
2) (2x+y)^2 - (x+2y)^2
= (2x + y + (x + 2y))(2x + y - (x + 2y))
= (3x + 3y)(x - y)
= 3(x + y)(x - y)
3) 4(2x+y)^2+4(2x+y)+1
= [2(2x + y)]^2 + 2[2(2x + y)][1] + 1^2
= [2(2x + y) + 1]^2
= (4x + 2y + 1)^2
2007-10-24 6:04 am
1) (2x-y)^2 -x^2
= (2x-y+x)(2x-y-x)
= (3x-y(x-y)
2) (2x+y)^2 - (x+2y)^2
= (2x+y+x+2y)(2x+y-x-2y)
= (3x+3y)(x-y)
= 3(x+y)(x-y)
3) 4(2x+y)^2+4(2x+y)+1
=[2(2x+y)]^2 + 2[2(2x+y)] + 1^2
=[2(2x+y)+1]^2
=(4x+2y+1)^2
= (2x-y+x)(2x-y-x)
= (3x-y(x-y)
2) (2x+y)^2 - (x+2y)^2
= (2x+y+x+2y)(2x+y-x-2y)
= (3x+3y)(x-y)
= 3(x+y)(x-y)
3) 4(2x+y)^2+4(2x+y)+1
=[2(2x+y)]^2 + 2[2(2x+y)] + 1^2
=[2(2x+y)+1]^2
=(4x+2y+1)^2
2007-10-24 6:04 am
1) (2x-y)^2 -x^2
= (2x-y+x)(2x-y-x)
= (3x-y(x-y)
2) (2x+y)^2 - (x+2y)^2
= (2x+y+x+2y)(2x+y-x-2y)
= (3x+3y)(x-y)
= 3(x+y)(x-y)
3) 4(2x+y)^2+4(2x+y)+1
=[2(2x+y)]^2 + 2[2(2x+y)] + 1^2
=[2(2x+y)+1]^2
=(4x+2y+1)^2
= (2x-y+x)(2x-y-x)
= (3x-y(x-y)
2) (2x+y)^2 - (x+2y)^2
= (2x+y+x+2y)(2x+y-x-2y)
= (3x+3y)(x-y)
= 3(x+y)(x-y)
3) 4(2x+y)^2+4(2x+y)+1
=[2(2x+y)]^2 + 2[2(2x+y)] + 1^2
=[2(2x+y)+1]^2
=(4x+2y+1)^2
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