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Question

Question 5
Factorise:
(i) 4x2+9y2+16z2+12xy24yz16xz(ii) 2x2+y2+8z222xy+42yz8xz

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Solution

(i) 4x2+9y2+16z2+12xy24yz16xz
Using identity (a+b+c)2=a2+b2+c2+2ab+2bc+2ca
(2x)2+(3y)2+(4z)2+2(2x)(3y)+2(3y)(4z)+2(4z)(2x)=(2x+3y4z)2=(2x+3y4z)(2x+3y4z)

(ii) 2x2+y2+8z222xy+42yz8xzUsing the identity (a+b+c)2=a2+b2+c2+2ab+2bc+2ca=(2x)2+(y)2+(22z)2+2(2x)(y)+2(y)(22z)+2(2x)(22z)=(2xy22z)2=(2xy22z)(2xy22z)

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