Expand each of the following,using suitable identities: (x+2y+4z)square
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(x+2y+4z)² is in the form of (a+b+c)²
As,(a+b+c)²=a²+b²+c²+2ab+2bc+2ca
⇒(x+2y+4z)²=x²+(2y)²+(4z)²+2(x)(2y)+2(2y)(4z)+2(4z)(x)
⇒(x+2y+4z)²=x²+4y²+16z²+4xy+16yz+8zx
As,(a+b+c)²=a²+b²+c²+2ab+2bc+2ca
⇒(x+2y+4z)²=x²+(2y)²+(4z)²+2(x)(2y)+2(2y)(4z)+2(4z)(x)
⇒(x+2y+4z)²=x²+4y²+16z²+4xy+16yz+8zx
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