F.3 Mathematics --- Factorization

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]

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