Question

Thực hiện phép tính:
\(\left(a^4+a^3b+a^2b^2+ab^3+b^4\right)\left(a-b\right)\)

Answer 1

\(=a^5+a^4b+a^3b^2+a^2b^3+ab^4-ab^4-a^3b^2-ab^4-b^5\\ =a^5-b^5\)

Answer 2

... =  \(\left[a^3\left(a+b\right)+b^2\left(a^2+ab+b^2\right)\right]\left(a-b\right)\) 

=  \(a^3\left(a^2-b^2\right)+b^2\left(a^3-b^3\right)=a^5-b^5\)

Answer 3

\(\left(a^4+a^3b+a^2b^2+ab^3+b^4\right)\left(a-b\right)\)

\(=a\left(a^4+a^3b+a^2b^2+ab^3+b^4\right)-b\left(a^4+a^3b+a^2b^2+ab^3+b^4\right)\)

\(=a^5+a^4b+a^3b^2+a^2b^3+ab^4-\left(ab^4+a^3b^2+a^2b^3+ab^4+b^5\right)\)

\(=a^5+a^4b+a^3b^2+a^2b^3+ab^4-ab^4-a^3b^2-a^2b^3-ab^4-b^5\)

\(=a^5-b^5\)