Question

show that (a-b)(a+b)+(b-c)(b+c)+(ç-a)(c+a)=0​

Answer 1

Show that (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0

Let's take the numbers in simple,

• a = 1

• b = 0

• c = 1

= ( 1 - 0 ) ( 1 + 0 ) ( 0 - 1 ) ( 0 + 1 ) ( 1 - 1 ) ( 1 + 1 )

= ( 1 ) ( 1 ) ( -1 ) ( 1 ) ( 0 ) ( 2 )

= 1 × 1 × ( - 1 ) × 1 × 0 × 2

= 0

As we already know that any number multiplied by 0 is 0, Either that number may be positive or negative, big or small 0 × any number is always 0.