Question

(xyz-4)(xyz-2) Use identity

Answer 1

Given expression:-

(xyz-4) (xyz-2)

using identity 4 = (x+a)(x+b) = x² + (a+b)x+ab

(xyz)² + (-4-2)xyz +-4×-2

x²y²z² - 6xyz - 8

Answer 2

Given,

(xyz-4)(xyz-2)

To find,

The solution of (xyz-4)(xyz-2) using an identity.

Solution,

After solving (xyz-4)(xyz-2) using an appropriate identity we will get (x²y²z² - 6xyz + 8).

We can easily solve this problem by following the given steps.

If we carefully observe the given expression, we will find that xyz is the same in both terms. So, the appropriate identity will be (x-a) (x-b).

(x-a) (x-b) = x² + (a+b)x + ab

In this case, we have x = xyz, a = -4 and b = -2.

Using the identity,

(xyz-4)(xyz-2) = (xyz)² + (-4-2)xyz + (-4×-2)

(xyz-4)(xyz-2) = x²y²z² -6xyz + 8

( Note that if the two integers are negative then they are added but the sign remains negative in the result. And the two negative integers in the multiplication gives a positive integer.)

Hence, after solving (xyz-4)(xyz-2) using an appropriate identity we get (x²y²z² - 6xyz + 8).