Question

A^2(A-B)^2-B^2(A+B)^2 分解因式

请帮忙啊..谢谢啦..

Answer 1

A²(A-B)²-B²(A+B)²
=[A(A-B)]²-[B(A+B)]² .....[用平方差公式：a²-b²=(a+b)(a-b)]
=[A²-AB]²-[AB+B²]²
=[(A²-AB)+(AB+B²)][(A²-AB)-(AB+B²)]
=[A²-AB+AB+B²][A²-AB-AB-B²]
=(A²+B²)(A²-2AB-B²)

Answer 2

A^2(A-B)^2-B^2(A+B)^2
=A^2(A^2-2AB+B^2)-B^2(A^2+2AB+B^2)
=A^4-2A^3B+A^2B^2-A^2B^2-2AB^3-B^4
=(A^4-B^4)-2AB(A^2+B^2)
=(A^2+B^2)(A^2-B^2)-2AB(A^2+B^2)
=(A^2+B^2)(A^2-2AB-B^2)

Answer 3

A^2(A-B)^2-B^2(A+B)^2 = [A(A-B)]^2 - [B(A+B)]^2 =[A(A-B)+B(A+B)][A(A-B)-B(A+B)] =(A^2+B^2)(A^2-2AB-B^2)

Answer 4

（a-b/2)^2-(a+b/2)^2
=(a-b/2+a+b/2)(a-b/2-a-b/2)
=2a*(-b)
=-2ab
就是平方差公式即可。把a-b/2看作是公式里的A，a+b/2看作公式里的B，所以符合A^2-B^2=(A+B)(A-B)

Answer 5

a^2+a-b^2-b=a^2-b^2+a-b=（a+b）（a-b）+a-b=（a-b）（a+b+1）

Answer 6

A²(A-B)²-B²(A+B)²
=[A(A-B)]²-[B(A+B)]²
.....[用平方差公式：a²-b²=(a+b)(a-b)]
=[A²-AB]²-[AB+B²]²
=[(A²-AB)+(AB+B²)][(A²-AB)-(AB+B²)]
=[A²-AB+AB+B²][A²-AB-AB-B²]
=(A²+B²)(A²-2AB-B²)