Factorize 1/27(2x 5y)3 -5/3y 3/4z)3 - 3/4z 2/3x)3?

Question

Factorize 1/27(2x   5y)3   -5/3y 3/4z)3 - 3/4z   2/3x)3?

Answer

Factorizing 1/27(2x 5y)3 -5/3y 3/4z)3 - 3/4z 2/3x)3

Given expression: 1/27(2x 5y)3 -5/3y 3/4z)3 - 3/4z 2/3x)3

Step 1: Identify the common factors

We can see that each term in the expression contains a common factor of (2x 5y)3. So, we can factorize this common factor out:

1/27(2x 5y)3 -5/3y 3/4z)3 - 3/4z 2/3x)3 = (2x 5y)3(1/27 - 5/3y 3/4z/(2x 5y)3 - 3/4z 2/3x/(2x 5y)3)

Step 2: Simplify the fraction

To simplify the fraction, we need to find a common denominator. The least common multiple of 2, 3, and 4 is 12. So, we can write:

-5/3y 3/4z = -20/12y 3/4z = -5/3y 9/12z = -5/4y 3/4z

Similarly,

3/4z 2/3x = 9/12z 8/12x = 3/4z 2/3x

Step 3: Final factorization

Substituting the simplified fractions in the expression, we get:

(2x 5y)3(1/27 - 5/4y 3/4z/(2x 5y)3 - 3/4z 2/3x/(2x 5y)3)

This is the final factorization of the given expression.

Answer