If (x + y + z = 0), then what is (x + y) (y + z) (z + x) equal to?

Correct Answer is : –xyz–xyz–xyz

Correct Answer is : –xyz–xyz–xyz

Test Index

RRB NTPC Mains or Stage 2 Model Paper 5 with solutions

Question : 17 of 120

Marks: +1, -0

(x + y + z = 0),

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

equal to?

Solution:

Concept:

Use

x+y+z=0

to write each pair-sum as the negative of the remaining variable.

Explanation:

Given:

x+y+z=0

So,

x+y=-z

Similarly,

y+z=-x

and

z+x=-y

Substitute these values:

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

There are three negative factors, so the product is negative.

Thus,

(-z)(-x)(-y)=-xyz

Answer:

-xyz

Go to Question:

Prev Question

Next Question