推导a^2-b^2=(a+b)(a-b)和(a-b)^2=a^2-2ab+b^2和(a+b)^2=a^2+2ab+b^2可以配上图吗

Question

推导a^2-b^2=(a+b)(a-b)和(a-b)^2=a^2-2ab+b^2和(a+b)^2=a^2+2ab+b^2
可以配上图吗

Answer 1

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