Expand eai!h of the following, using suitable Uhntiti.e8: (i) (x + 2y + 4zf (j.i) (2x -y + zJ2 (iii} (- 2x + Sy + 2zJ2 (iv) (3a - 7b -cf <- :zx + sy - szf [a-jb+1 T .

(i) (% + 2y + 4z>2 = (x'f + (2y>2 + (4z)2 + 2(%)(2y) + 2(2y)(4t) + 2(.x)(4z) [Using identity: (x + y + z'f = r2 + y2 + z2 + 2%y + 2yz + 2ix] = r2 + 4y2 + 16z2 + 4%y + 16yz + 8.u. (iz. (2.% -y + z'?- .. (2.%>2 + (-y1' + >2 + 2(2.%)(- y) + 2(- yXz> + 2(2%Xz) [Using identity: (x + y + z>2 • r2 + y2 + z2 + 2%y + 2yz + 2.u] = .4%2 + y2 + z2 - 4.%y - 2yz + 4u. (iizj (- 2.% + 3y + 2z>2 = (- 2.%)2 + (3y1' + (2z)2 + 2(- 2.%)(3y) + 2(3y)(2z) + 2(- 2.%X2i) [Using identity: (x + y + z'f = r2 + y2 + z2 + 2%y + 2yz + 2u] = 4%2 + 9y2 + 4.r - 12%)' + 12yz - Srz. (iv) (3a - 7b - c>2 = (3a1' + (- 7b>2 + (- c>2 + 2(3a)(- 7b) + 2(- 7b)(- c) + 2(3a)(- c) [Using identity: (% + y + z1' = r2 + y2 + z2 + 2%y + 2yz + 2.u] = 9a2 + 49b2 + c2 - 42ab + 14bc - Gae. P a. YNor.tALS 39 (v) (- 2x + 6y - &>2 = (- 2x'f + (5y)2 + (- &)2 + 2(- 2x)(6y)+ 2(5,Y,X- Sz) + 2(- 2xX- 3z) CUsing identity: (x + y + z)2 c r2 + y2 + z2 + 2xy + 2yz + 2.u] = 4%2 + 25y2 + 9z2 - 20xy - 30yz + 12u. (vi) [o-ib+lr = (ar + (-ibJ + (1>2 + 2(a)(-ib)+ 2(-jb)cl) + 2(a)<1) [Using identity: (% + y + z'f = r2 + y2 + z2 + 2xy + 2yz + 2.u] = ..!.a2 + .!.b2 + 1- .!.ab - b + .!.a