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Question

Factorize
25x2+16y2+4z240xy+16yz20xz

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Solution

25x2+16y2+4z240xy+16yz20xz
= (5x)2+(4y)2+(2z)2+2(5x)(4y)+2(4y)(2z)+2(5x)(2z)
Suitable identities is (x+y+z)2=x2+y2+z2+2xy+2yz+2xz
Therefore, (5x)2+(4y)2+(2z)2+2(5x)(4y)+2(4y)(2z)+2(5x)(2z)
= (5x+4y+2z)2

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