Question

5. (x - y) (x + y) + (y - z) (y + z) + (z - x) (z + x) is equal to ___________________.​

Answer 1

$\huge\star\underline{\mathtt\red{A}\mathtt\green{N}\mathtt\blue{S}\mathtt\purple{W}\mathtt\orange{E}\mathtt\pink{R}}\star\:$

Q1. (x - y) (x + y) + (y - z) (y + z) + (z - x) (z + x)

Now, we will solve this by using the identity i.e.,

(a + b)(a - b) = (a)² - (b)²

=> (x - y) (x + y) + (y - z) (y + z) + (z - x) (z + x)

=> (x)² - (y)² + (y)² - (z)² + (z)² - (x)²

=> Putting the like terms together we get :-

=> (x)² - (x)² - (y)² + (y)² - (z)² + (z)²

=> ${\cancel{(x)² - (x)² - (y)² + (y)² - (z)² + (z)²}}$

✒ 0

Answer 2

Answer:

(x - y) (x + y) + (y - z) (y + z) + (z - x) (z + x) is equal to 0.

Step-by-step explanation:

Solution-

Formula-

• $\tt\red{(a+b)(a-b)=(a-b)² }$

ㅤ

Evaluating-

=${(x - y) (x + y)} + {(y - z) (y + z)} + {(z - x) (z + x)}$

=${(x-y) ²} +{(y-z)²} +{(z-x) ²}$

=$\cancel{x² - y² +y² - z² +z² - x²}$

= 0