Question

几道数学因式分解 a八次-2a四次+1 (2)-2/3ax平方+4ax-6a (3) -6(2a-b)平方-4(2a-b)

(4) 4m²(x+y)²-12mn(x+y)(x-y)+9n²(x-y)²

Answer 1

a八次-2a四次+1
=(a的4次方-1)²
=(a²+1)²(a+1)²(a-1)²

(2)-2/3ax平方+4ax-6a
=-2/3a(x²-6x+9)
=-2/3a(x-3)²

(3) -6(2a-b)平方-4(2a-b)
=-2(2a-b)(6a-3b+2)

(4) 4m²(x+y)²-12mn(x+y)(x-y)+9n²(x-y)²
=[2m(x+y)+3n(x-y)]²
=(2mx+2my+3nx-3ny)²

追问

还有两道，25（a-b)平方-9（a+b)平方
（2）16/25x四次-9/16y平方，回答出来就你了

追答

先采纳，再求助

Answer 2

(1)a^8-2a^4+1
=(a^4-1)²
=[(a²+1)(a²-1)]²
=[(a²+1)(a+1)(a-1)]²
=(a²+1)²(a+1)²(a-1)²

(2)-2/3ax²+4ax-6a
=-2/3a(x²-6x+9)
=-2/3a(x-3)²

(3)-6(2a-b)²-4(2a-b)
=-2(2a-b)[3(2a-3)-2]
=-2(2a-b)(6a-11)

(4)4m²(x+y)²-12mn(x+y)(x-y)+9n²(x-y)²
=[2m(x+y)]²-2[2m(x+y)][3n(x-y)]+[3n(x-y)]²
=[2m(x+y)-3n(x-y)]²
=(2mx+2my-3nx+3ny)²

Answer 3

25（a-b）^2-9(a+b)^2
= [5(a-b)]^2-[3(a+b)]^2
= [5(a-b)+3(a+b)][5(a-b)-3(a+b)]
= (8a-2b)(2a-8b)
= 4(4a-b)(a-4b)
16/25x^4-9/16y^2
=(4/5x^2)^2-(3/4y)^2
=(4/5x^2+3/4y)(4/5x^2-3/4y)