a3+a2b-ab2-b3,八年级上册因式分解!

Question

a的三次方加a的二次方b减ab的二次方减b的三次方

Answer 1

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

Answer 2

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

Answer 3

a3+a2b-ab2-b3=a2(a+b)-b2(a+b)=(a2-b2)(a+b)=(a-b)(a+b)2

Answer 4

a³+a²b-ab²-b³
=a²(a+b)-b²(a+b)
=(a²-b²)(a+b)
=(a-b)(a+b)²

Answer 5

a^3+a^2b+ab^2+b^3
=a^2(a+b)+b^2(a+b)
=(a+b)(a^2+b^2)