Question

 

Bài 2 Chứng minh hằng đẳng thức 

a. (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2ac + 2bc

b. (a + b) 2 + (a − b) 2 = 2a 2 + 2b 2 . 

c. (a + b) 2 − (a − b) 2 = 4ab.

 

Answer 1

a, \(\left(a+b+c\right)^2=\left[\left(a+b\right)+c\right]^2=\left(a+b\right)^2+2c\left(a+b\right)+c^2=a^2+b^2+c^2+2ab+2ac+2bc\)

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

c, \(\left(a+b\right)^2-\left(a-b\right)^2=\left(a+b-a+b\right)\left(a+b+a-b\right)=2b.2a=4ab\)

Answer 2

\(\left(a+b+c\right)^2=\left[\left(a+b\right)+c\right]^2=\left(a+b\right)^2+2\cdot\left(a+b\right)\cdot c+c^2\\ =a^2+2ab+b^2+2ac+2bc+c^2\\ =a^2+b^2+c^2+2ab+2ac+2bc\)

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

\(\left(a+b\right)^2-\left(a-b\right)^2=\left(a+b+a-b\right)\left(a+b-a+b\right)\\ =2a\cdot2b=4ab\)

Answer 3

a) (a+b+c)² = (a+b)² + 2(a+b)c + c² = a² + 2ab +b² + 2ac+ 2bc+ c²

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

c) (a+b)²- (a-b)² = a²+ 2ab+ b²- a²+ 2ab- b² = 4ab