Find the HCF from 9m^2 - 4n^2 - 4nr - r^2, r^2 - 4n^2 - 9m^2 - 12mn, and 9m^2 + 6mr + r^2 - 4n^2

1st expression: 9m² - 4n² - 4nr - r²
= 9m² - {(2n)² + 2.2nr + r²}
= 9m² - (2n + r)²
= (3m)² - (2n + r)²
= (3m + 2n + r)(3m - 2n - r)

2nd expression: r² - 4n² - 9m² - 12mn
= r² - {(2n)² + (3m)² + 2.2n.3m}
= r² - (2n + 3m)²
= (r + 2n + 3m)(r - 2n - 3m)

3rd expression: 9m² + 6mr 9 r² - 4n²
= (3m + r)² - (2n)²
= (3m + r + 2n)(3m + r - 2n)

Above expressions, common factor is (3m + r + 2n). So, the HCF is (3m + r + 2n).

And here is the video explanation.