Question

What is the Highest Common Factor (H.C.F) of the expressions 9x² – 4y² – 8yz – 4z², 4z² - 4y² - 9x² - 12xy and 9x² + 12xz + 4z² - 4y²​

a)3x+2y-2z
b)3x-2y+2z
c)2x-3y+2z
d)2x+3y-2z

Answer 1

The Highest Common Factor of the given expressions is (3x + 2z)(y + 2z).

Step-by-step explanation:

To find the Highest Common Factor (H.C.F) of the given expressions, we need to factorize each expression and find the common factors.

1. 9x² – 4y² – 8yz – 4z² can be factorized as (3x - 2y)(3x + 2y) - 4z(y + 2z).

2. 4z² - 4y² - 9x² - 12xy can be factorized as (2z - 2y - 3x)(2z + 2y + 3x).

3. 9x² + 12xz + 4z² - 4y² can be factorized as (3x + 2z)(3x + 2z) - 4y(y + 2z).

After factorizing, we can see that the common factors among these expressions are (3x + 2z) and (y + 2z). Therefore, the H.C.F is (3x + 2z)(y + 2z).