Question

Expand the following using suitable identites :(x+2y+4z)2, (1/4a -1/2b +1)2,(2x+ 3y+2z)2

Answer 1

${(x + 2y + 4z)}^{2} = {x}^{2} + 4 {y}^{2} + 16 {z}^{2} + 2x(2y) + 2(2y)(4z) + 2x(4z) \\ = {x }^{2} + 4 {y}^{2} + 16 {z}^{2} + 4xy + 16yz + 8xz$
$( { \frac{1}{4} a - \frac{1}{2} b + 1)}^{2} \\ = \frac{1}{16} {a}^{2} + \frac{1}{4} {b}^{2} + 1 + 2( \frac{1}{4} )a( \frac{ - 1}{2}) b + 2 (\frac{ - 1}{2}) b(1) + 2 \frac{1}{4} a(1) \\ = \frac{1}{16} {a}^{2} + \frac{1}{4} {b}^{2} + 1 - \frac{1}{4} ab - b + \frac{1}{2}a$
$( {2x + 3y + 2z)}^{2} \\ = 4 {x}^{2} + 9 {y}^{2} + 4 {z}^{2} + 2(2x)(3y) + 2(3y)(2z) + 2(2x)(2z) \\ = 4 {x}^{2} + 9 {y}^{2} + 4 {z}^{2} + 12xy + 12yz + 8xz$