Question

Tính: (a-b)(a^2+3ab+b^2)+(a+b)^3+ab(b-a)

Answer 1

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

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

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

Answer 2

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

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

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

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

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

\(=\left(a+b\right)^2.2a\)

Answer 3

(a - b)(a² + 3ab + b²) + (a + b)³ + ab(b - a)

= a(a² + 3ab + b²) - b(a² + 3ab + b²) + (a + b)(a² + 2ab + b²) + ab(b - a)

= a³ + 3a²b + ab² - ba² - 3b²a - b³ + a² + 2a²b + ab² + ba² + 2b²a + b³ + ab² - a²b

= (a³ + a³) + (3a²b - a²b + 2a²b + a²b - a²b) + (ab² - 3ab² + ab² + 2ab² + ab²) + (-b³ + b³)

= 2a² + 4a²b + 2ab²

Answer 4

tại sao ra được -ab vậy bạn