# 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

help me with this pls. I'm so stucked

Go to main content# 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

help me with this pls. I'm so stucked

1st expression: 9m^{2} - 4n^{2} - 4nr - r^{2}

= 9m^{2 } - {(2n)^{2} + 2.2nr + r^{2}}

= 9m^{2} - (2n + r)^{2}

= (3m)^{2} - (2n + r)^{2}

= (3m + 2n + r)(3m - 2n - r)

2nd expression: r^{2} - 4n^{2} - 9m^{2} - 12mn

= r^{2} - {(2n)^{2} + (3m)^{2} + 2.2n.3m}

= r^{2} - (2n + 3m)^{2}

= (r + 2n + 3m)(r - 2n - 3m)

3rd expression: 9m^{2} + 6mr 9 r^{2} - 4n^{2}

= (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.