28(x+y)^2 - 7(x-y)^2
Please help me to factorize the above expression with detailed steps!
Thanks!
F.3 Mathematics --- Factorization
2008-09-03 11:32 pm
回答 (2)
2008-09-04 1:38 am
✔ 最佳答案
公式一: a^2-b^2 = (a-b)(a+b)28(x+y)^2 - 7(x-y)^2
= 7 [ 4(x+y)^2-(x-y)^2]
Let a= 2(x+y) , b=(x-y)
7[4(x+y)^2 - (x-y)^2]
= 7[a^2-b^2]
= 7(a-b)(a+b)
= 7[2x+2y-x+y][2x+2y+x-y]
= 7[x+3y][3x+y]
2008-09-03 11:52 pm
If you want to solve the above Factorization, Please remember the follow formule
(x+y)^2 = x^2+2xy+y^2
(x-y)^2 = x^2-2xy+y^2
SO
28(x+y)^2 - 7(x-y)^2
=28(x^2+2xy+y^2) - 7(x^2-2xy+y^2)
=7*4(x^2+2xy+y^2) - 7(x^2-2xy+y^2)
=7(4x^2+8xy+y^2-x^2+2xy-y^2)
=7(3x^2+10xy+3y^2)
=7(3x+y)(3y+x)
Factorization就是先把所有野拆散，然後再重新找相似加以整合
(x+y)^2 = x^2+2xy+y^2
(x-y)^2 = x^2-2xy+y^2
SO
28(x+y)^2 - 7(x-y)^2
=28(x^2+2xy+y^2) - 7(x^2-2xy+y^2)
=7*4(x^2+2xy+y^2) - 7(x^2-2xy+y^2)
=7(4x^2+8xy+y^2-x^2+2xy-y^2)
=7(3x^2+10xy+3y^2)
=7(3x+y)(3y+x)
Factorization就是先把所有野拆散，然後再重新找相似加以整合
收錄日期: 2021-05-01 15:32:44
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