Question

Simplify the following expression:
(i) (x + y + z)(x + y – z)

Answer 1

Answer:

The simplified form of (x + y + z)(x + y – z) is x² + y² - z² + 2xy

Step-by-step explanation:

We have to simplify (x + y + z)(x + y – z)

Let x + y = a

Putting x + y = a in (x + y + z)(x + y – z) we get,

(a + z) (a - z)

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

= a² - z²

Now, we know a = x + y

So, a² - z² = (x + y)² - z²

Using identity (a + b)² = a² + b² + 2ab  in (x + y)²

= x² + y² + 2xy - z²

= x² + y² - z² + 2xy

So, the simplified form of (x + y + z)(x + y – z) is x² + y² - z² + 2xy