Question

(a+b)^2-2(a+b)

a(x-y)+b(y-x)+c(x-y) (x+2)^2-9 4(a+b)^2-9(a-b)^2 80a^2(a+b)-45b^2(a+b)

Answer 1

a+b)^2-2(a+b)
=(a+b)(a+b-2)

追问

a(x-y)+b(y-x)+c(x-y) (x+2)^2-9 4(a+b)^2-9(a-b)^2 80a^2(a+b)-45b^2(a+b)

追答

a(x-y)+b(y-x)+c(x-y)
=(x-y)(a-b+c)
(x+2)^2-9
=(x+2+3)(x+2-3)
=(x+5)(x-1)
4(a+b)^2-9(a-b)^2
=[2(a+b)+3(a-b)][ 2(a+b)-3(a-b)]
=(5a-b)(-a+5b)
80a^2(a+b)-45b^2(a+b)
=5(a+b)(4a+3b)(4a-3b)

追问

(x+y)^2-4(x^2-y^2)+4(x-y)^2 16a^4-8a^2+1 (x^2+4)^2-16x^2 4x^2-y^2-2y-1

追答

(x+y)^2-4(x^2-y^2)+4(x-y)^2
=(x+y-2x+2y)^2
=(3y-x)^2
16a^4-8a^2+1
=(4a-1)^2
(x^2+4)^2-16x^2
=(x^2+4+4x)(x^2+4-4x)
=(x+2)^2(x-2)^2
4x^2-y^2-2y-1
=4x^2-(y+1)^2
=(2x+y+1)(2x-y-1)

Answer 2

(a+b)^2-2(a+b)
=（a+b)[(a+b)-2]
=(a+b)(a+b-2)