# 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)2

= (2x + 3y – 4z) (2x + 3y – 4z)

(ii) Using identity,

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

2x2 + y2 + 8z2 - 2√2xy + 4√2yz – 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)

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