Question

The value of (x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x) is:The value of (x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x) is:​

Answer 1

To Evaluate :

The value of :

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

Identity To Be Used:

We will use the following identity of expressions:

• (a-b)(a+b) = a²-b²

Solution :

Now here, the terms can be simplified by using the identity given above :

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

= (x²-y²) + (y²-z²) + (z²-x²)

= (x²-x²)+(y²-y²)+(z²-z²)

= 0+0+0

= 0

So, the value of :

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

= 0

Additional Information:

Some Identities useful for these kinds of questions :

• (a+b)² = a²+b+2ab
• (a-b)² = a²+b²-2ab
• (x+a)(x+b) = x²+(a+b)x+ab
• (a+b+c)³ = a²+b²+c²+2ab+2bc+2ca
• (a+b)³ = a³+b³+3a²b+3ab²
• (a-b)³ = a³-b³-3a²b+3ab²
• (a+b)(a-b) = a²-b²

Answer 2

The answer is Z(zed) E(ee) R(ar) O(o)

Means 0, the invention of Aryabhatt