Expand each of the following, using suitable identities: (i)(x+2y+4z)² (ii)(2x−y+z)² (iii)(−x+3y+2z)² (iv)(3a−7b−c)² (v)(−x+5y−z)² (vi)(1/4a−b+1)²

We know,(a+b+c)²=a²+b²+c²+2ab+2bc+2aci
(i)(x+2y+4z)²=x²+(2y)²+(4z)²+2(x)(2y)+2(2y)(4z)+2(x)(4z)=x²+4y²+16z²+4xy+16yz+8xz
(ii)(2x−y+z)²=(2x)²+(−y)²+(z)²+2(2x)(−y)+2(−y)(z)+2(2x)(z)=4x²+y²+z²−4xy−2yz+4xz
(iii)(−x+3y+2z)²=(−x)²+(3y)²+(2z)²+2(−x)(3y)+2(3y)(2z)+2(−x)(2z)=x²+9y²+4z²−6xy+12yz−4xz
(iv)(3a−7b−c)²=(3a)²+(−7b)²+(−c)²+2(3a)(−7b)+2(−7b)(−c)+2(3a)(−c)=9a²+49b²+c²−42ab+14bc−6ac
(v)(−x+5y−z)²=(−x)²+(5y)²+(−z)²+2(−x)(5y)+2(5y)(−z)+2(−z)(−x)=x²+25y²+z²−10xy−10yz+2xz
(vi)(1/4a−b+1)²=(1/4a)²+(−b)²+(1)²+2(1/4a)(−b)+2(−b)(1)+2(1/4a)(1)=1/16a²+b²+1−1/2ab−2b+1/2a