Question

phan tich da thuc thanh nhan tu

(a+b)³-(a-b)³

Answer 1

Đặt A = a + b ; B = a - b
A^3 + B^3
= (A + B)(A² - AB + B² )
= (a + b + a - b)[(a + b)² - (a + b)(a - b) + (a - b)²]
= 2a( a² + 2ab + b² - a² + b² + a² - 2ab + b² )
= 2a( a² + 3b²)

Answer 2

(a+b)\(^3\) - (a-b)\(^3\)

= [ (a+b) - (a-b) ] [ (a+b)\(^2\) + (a+b)(a-b) + (a-b)\(^2\) ]

= [ a+b - a+b ] [ a\(^2\) + 2ab + b\(^2\) + a\(^2\) - b\(^2\) + a\(^2\) - 2ab + b\(^2\) ]

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