Question

Chứng minh rằng:

a) (a+b)²=(a-b)²+4ab

b)(a-b)²=(a+b)²-4ab

c) a³+b³=(a+b)³-3ab(a+b)

Answer 1

a) VP= (a-b)^2 + 4ab 

= a^2 - 2ab + b^2 + 4ab

= a^2 + 2ab + b^2 

= (a+b)^2 = VT

Vậy ...

b) VP= (a+b)^2 - 4ab 

= a^2 + 2ab + b^2 - 4ab

= a^2 - 2ab + b^2

= (a-b)^2 = VT

Vậy....

c) VP= (a+b)^3 - 3ab (a+b) 

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

= a^3 + b^3  = VT

Vậy ....

Answer 2

a) Ta có: \(\left(a-b\right)^2+4ab=a^2-2ab+b^2+4ab=a^2+2ab+b^2=\left(a+b\right)^2\)

Vậy: (a+b)² = (a-b)² + 4ab.

b) Ta có: \(\left(a+b\right)^2-4ab=a^2+2ab+b^2-4ab=a^2-2ab+b^2=\left(a-b\right)^2\)

Vậy: (a-b)² = (a+b)² - 4ab

c) Ta có:  \(\left(a+b\right)^3-3ab\left(a+b\right)=a^3+3a^2b+3ab^2+b^3-3a^2b-3ab^2=a^3+b^3\)

Vậy: a³ + b³ = (a+b)³ - 3ab(a+b)

Đúng nha!!