Question

simplify : (x-y)(x+y) + (y-z)(y+z) + (z-x)(z+x) =_____​

Answer 1

Answer:

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

=xy-xz+yz-yx+zx-zy

=0

Step-by-step explanation:

hey mate! here u go （＾ｖ＾）

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

=xy-xz+yz-xy+xz-yz

=(xy-xy)+(-xz+xz)+(yz-yz)

=(0)+(0)+(0)

=0

Answer 2

(x-y)(x+y) + (y-z)(y+z) + (z-x)(z+x) = 0

Given:

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

To Find:

• Simplify

Solution:

• (a - b)(a + b) = a² - b²

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

Step 1:

Apply identity (a - b)(a + b) = a² - b²

= x² - y²  + y²  - z² + z² - x²

Step 2:

Combine like term

= x² - x² - y²  + y²  - z² + z²

Step 3:

Cancel the opposite terms

= 0 + 0  + 0

= 0

Hence,  (x-y)(x+y) + (y-z)(y+z) + (z-x)(z+x) = 0