সূত্রের সাহায্যে বর্গ নির্ণয় কর

a + 5 এর বর্গ $=(a+5{)}^2=(a{)}^2+2\times a\times 5+(5{)}^2$

                      $=a^2+10a+25$

5x - 7 এর বর্গ $=(5x-7{)}^2$

                       $=(5x{)}^2-2\times 5x\times 7+(7{)}^2$

                       $=25x^2-70x+49$

3a - 11xy এর বর্গ $=(3a-11xy{)}^2$

                            $=(3a{)}^2-2\times 3a\times 11xy+(11xy{)}^2$

                            $=9a^2-66axy+121x^2{y}^2.$

$5a^2+9m^2$ এর বর্গ = $(5a^2+9m^2{)}^2$

                                 $=(5a^2{)}^2+2\times 5a^2\times 9m^2+(9m^2{)}^2$

                                $=25a^4+90a^2{m}^2+81m^4$

990 এর বর্গ $=(990{)}^2=(1000-10{)}^2$

                   $=(1000{)}^2-2\times 1000\times 10+(10{)}^2$

                   = 1000000 - 20000 + 100

                   =1000100-20000

                   = 980100.

xy - 6y এর বর্গ $=(xy-6y{)}^2$

                          $=(xy{)}^2-2\times xy\times 6y+(6y{)}^2$

                         $=x^2{y}^2-12x{y}^2+36y^2.$

ax - by এর বর্গ $=(ax{)}^2-2\times ax\times by+(by{)}^2$

                          $= a^2{x}^2-2abxy + b^2{y}^2$

97 এর বর্গ $=(97{)}^2=(100-3{)}^2$

                  $=(100{)}^2-2\times 100\times 3+(3{)}^2$

                  = 10000 - 600 +9

                  = 10009-600 = 9409.

2x + y -z  এর বর্গ = $(2x+y-z{)}^2$

                            $=\left\{\right(2x+y)-z{\}}^2=(2x+y{)}^2-2x(2x+y) z+z^2$

                           $=(2x{)}^2+2\times 2x\times y+y^2-4zx-2yz+z^2$

                           $=4x^2+4xy+y^2-4zx-2yz+z^2$

                          $=4x^2+y^2+z^2+4xy-4zx-2yz.$

55 এর বর্গ $=(55{)}^2=(50+5{)}^2$

                $=(50{)}^2+2\times 50\times 5+(5{)}^2$

               = 2500 + 500 + 25 = 3025

2a - b +3c এর বর্গ

$=(2a-b+3c{)}^2=\{(2a-b)+3c{\}}^2$

$=(2a-b{)}^2+2(2a-b) 3c+(3c{)}^2$

$=(2a{)}^2-2\times 2a\times b+(b{)}^2+12ac-6bc+9c^2$

$=4a^2-4ab+b^2+12ac-6bc+9c^2$

$=4a^2+b^2+9c^2-4ab+12ac-6bc.$

$x^2+y^2-z^2$ এর বর্গ

$=(x^2+y^2-z^2{)}^2=\{(x^2+y^2)-z^2{\}}^2$

$=(x^2+y^2{)}^2-2(x^2+y^2) z^2+(z^2{)}^2$

$=(x^2{)}^2+2x^2{y}^2+(y^2{)}^2-2z^2*x^2-2y^2{z}^2+z^4$

$=x^4+2x^2{y}^2+y^4-2x^2*z^2-2y^2{z}^2+z^4$

$=x^4+y^4+z^4+2x^2{y}^2-2y^2{z}^2-2z^2{x}^2.$

a - 2b - c এর বর্গ

$=(a-2b-c{)}^2=\{(a-2b)-c{\}}^2$

$=(a-2b{)}^2-2(a-2b) c+(c{)}^2$

$=a^2-2\times a\times 2b+(2b{)}^2-2ca+4bc+c^2$

$=a^2-4ab+4b^2-2ca+4bc+c^2$

$=a^2+4b^2+c^2-4ab-2ac+4bc.$

3x - 2y + z এর বর্গ $= {(3x-2y + z)}^2$

$=\left\{\right(3x-2y)+z{\}}^2=(3x-2y{)}^2+2x(3x-2y) z+z^2$

$=(3x{)}^2-2\times 3x\times 2y+(2y{)}^2+6zx-4yz+z^2$

$=9x^2+4y^2+z^2-12xy.+6zx-4yz.$

bc + ca + ab এর বর্গ

$=(bc+ca+ab{)}^2=\{(bc+ca)+\left(ab\right){\}}^2$

$=(bc+ca{)}^2+2(bc+ca) ab+(ab{)}^2$

$=(bc{)}^2+2\times bc\times ca+(ca{)}^2+2a{b}^{2}c+2a^{2}bc+a^2{b}^2$

$= b^2{c}^2+c^2{a}^2 + a^2{b}^2 + 2ab{c}^2+ 2a{b}^{2}c + 2a^{2}bc.$

$2a^2 + 2b - c^2$ এর বর্গ

$=(2a^2+2b-c^2{)}^2=\{(2a^2+2b)-c^2{\}}^2$

$=(2a^2+2b{)}^2-2\times (2a^2+2b)c^2+(c^2{)}^2$

$=(2a^2{)}^2+2\times 2a^2\times 2b+(2b{)}^2-4c^2{a}^2-4b{c}^2+c^4$

$=4a^4+8a^{2}b+4b^2-4c^2{a}^2-4b{c}^2+c^4$

$=4a^4+4b^2+c^4+8a^{2}b-4$$ab{c}^2-4b{c}^2$