Question

关于立方和与立方差公式a^3+b^3=(a+b)(a^2-ab+b^2) a^3-b^3=(a+b)(a^2+ab+b^

Answer 1

a^3+b^3

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

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

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

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

a^3-b^3

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

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

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

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