Question

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Find the HCF of the following expressions...!

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Answer 1

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Answer....

THE HCF OF 4 X SQUARE - 12 X Y + 16 Z SQUARE - 24 Y Z + 16 Z X AND 8 X CUBE + 72 X Y Z + 64 Y CUBE MINUS 27 Y CUBE IS 1.....

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Answer 2

(i) 4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz

Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca 

4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz

= (2x)2 + (3y)2 + (-4z)2 + (2×2x×3y) + (2×3y×-4z) + (2×-4z×2x)

= (2x + 3y - 4z)2

=  (2x + 3y - 4z) (2x + 3y - 4z)

(ii) 2x2 + y2 + 8z2 - 2√2 xy + 4√2 yz - 8xz

Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

2x2 + y2 + 8z2 - 2√2 xy + 4√2 yz - 8xz 

= (-√2x)2 + (y)2 + (2√2z)2 + (2×-√2x×y) + (2×y×2√2z) + (2×2√2z×-√2x)

= (-√2x + y + 2√2z)2

=  (-√2x + y + 2√2z) (-√2x + y + 2√2z)