Question

Solve (x - y) (x + y) + (y - z) (y + z) + (z -x) (z + x)

(y + z)
zero
(x - y)
(z - x)​

Answer 1

Answer :

›»› The required answer is 0 (zero).

Given :

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

To Solve :

• Expand the expression.

Solution :

→ (x - y) (x + y) + (y - z) (y + z) + (z - x) (z + x)

Organize the expression with the distributive,

→ x² - y² + (y - z) (y + z) + (z - x) (z + x)

Organize the expression with the distributive law,

→ x² - y² + y² - z² + (z - x) (z + x)

Sort the polynomial expression in descending order,

→ x² - y² + y² - z² + (-x + z) (z + x)

Sort the polynomial expression in descending order,

→ x² - y² + y² - z² (-x + z) (x + z)

Organize the expression with the distributive,

→ x² - y² + y² - z² - x² + z²

Organize the similar term,

→ (1 - 1)x² + (-1 + 1)y² + (-1 + 1)z²

Arrange the constant term,

→ 0x² + (-1 + 1)y² + (-1 + 1)z²

If we multiply a number by 0, it becomes 0,

→ 0 + (-1 + 1)y² + (-1 + 1)z²

Arrange the constant term,

→ 0 + 0y² + (-1 + 1)z²

If we multiply a number by 0, it becomes 0,

→ 0 + 0 + (-1 + 1)z²

Arrange the constant term,

→ 0 + 0 + 0z²

If we multiply a number by 0, it becomes 0,

→ 0 + 0 + 0

Add 0 and 0,

→ 0 + 0

Again add 0 and 0,

→ 0

Hence, the required answer is 0 (zero).

So, option (b) zero is correct ✔.

Answer 2

Answer:

zero

Step-by-step explanation:

x2 - y2 + y2 - z2 + z2- x2

0 ( all gets cancelllled)

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