Factorise:
(i) 4x 2 + 9y 2 + 16z 2 + 12xy – 24yz – 16xz
(ii) 2x 2 + y 2 + 8z 2 – 2√2 xy + 4√2 yz – 8xz
Factorise:
(i) 4x 2 + 9y 2 + 16z 2 + 12xy – 24yz – 16xz
(ii) 2x 2 + y 2 + 8z 2 – 2√2 xy + 4√2 yz – 8xz
Solution and Explanation
(i) It is known that,
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz : (2x)2 + (3y)2 + (-4z)2 + 2(2x)(3y) + 2(3y)(-4z) + 2(2x)(-4z)
= (2x + 3y - 4z)2 = (2x + 3y - 4z)(2x + 3y - 4z)
(ii) 2x2 + y2 + 8z2 – 2√2xy + 4√2 yz – 8xz
= (-√2x)2 + (y)2 + (2√2z)2 + 2(-√2x) (y) + 2(y)(2√2z) + 2 (-√2x)(2√2z)
= (-√2x + y + 2√2z)2 = (-√2x + y + 2√2z) (-√2x + y + 2√2z)
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