Question

simplify (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)​

Answer 1

Answer:

Step-by-step explanation:

(a+b)(a-b)+(b+c)(b-c)+(c+a)(c-a),

=(a²-b²)+(b²-c²)+(c²-a²),

=(a²-b²+b²-c²+c²-a²),

In this case, each variable cancels it's negative version.

= 0

NOW, THAT'S THE CORRECT ANSWER.

Answer 2

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

Given :

(a + b)(a - b) + (b + c)(b - c) + (c + a)(c - a)

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

(a + b)(a - b) + (b + c)(b - c) + (c + a)(c - a)

Step 2 of 2 :

Find the value of the expression

We use

a² - b² = ( a + b ) ( a - b )

b² - c² = ( b + c ) ( b - c )

c² - a² = ( c + a ) ( c - a )

Hence the given expression

= (a + b)(a - b) + (b + c)(b - c) + (c + a)(c - a)

= a² - b² + b² - c² + c² - a²

= a² - a² + b² - b² + c² - c²

= 0 + 0 + 0

= 0

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