平方差公式分解因式 过程

Question

不要忘了过程
1.x^2-(a+b-c)^2
2.(a-b)(3a+b)^2+(a+3b)^2(b-a)

Answer 1

1.x^2-(a+b-c)^2
=(x+(a+b-c))(x-(a+b-c))
=(x+a+b-c)(x-a-b+c)

2.(a-b)(3a+b)^2+(a+3b)^2(b-a)
=(a-b)(3a+b)²-(a+3b)²(a-b)
=(a-b)[(3a+b)²-(a+3b)²]
=(a-b)[(3a+b+a+3b)(3a+b-a-3b)]
=(a-b)(4a+4b)(2a-2b)
=8(a-b)²(a+b)

Answer 2

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

(a-b)(3a+b)^2+(a+3b)^2(b-a)
=a(3a+b)^2-b(3a+b)^2+b(a+3b)^2-a(a+3b)^2
=a((3a+b)^2-(a+3b)^2)+b((a+3b)^2-(3a+b)^2)
=a(3a+b+a+3b)(3a+b-a-3b)+b(a+3b+3a+b)(a+3b-3a-b)
=8a(a+b)(a-b)-8b(a+b)(a-b)
=8(a+b)(a-b)^2

Answer 3

1.原式=(x-a-b+c)(x+a+b-c)

2.原式=(a-b)(3a+b)^2-(a+3b)^2(a-b)
=(a-b)[(3a+b)^2-(a+3b)^2]
=(a-b)(2a-2b)(4a+4b)