Factorize:

(i)


(ii)


(i) 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 * 2 * 3y) + (2 * 3y * -4z) + (2 * -4z * 2x)+= (2x + 3y – 4z)


= (2x + 3y – 4z)2


= (2x + 3y – 4z) (2x + 3y – 4z)


(ii) Using identity,


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


2x2 + y2 + 8z2 - 2xy + 4yz – 8xz


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


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