সূত্রের সাহায্যে নিচের রাশিগুলোর বর্গ নির্ণয় কর :

5a + 7b এর বর্গ $=(5a+7b{)}^2$

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

$=25a^2+70ab+49b^2$ (Ans.)

5a + 7b এর বর্গ $=(5a+7b{)}^2$

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

$=25a^2+70ab+49b^2$ (Ans.)

7p - 2q এর বর্গ $=(7p-2q{)}^2$

$=(7p{)}^2-2\times 7p\times 2q+(2q{)}^2$

$=49p^2-28pq+4q^2$

ax - by এর বর্গ $=(ax-by{)}^2$

$=(ax{)}^2-2axby+(by{)}^2$

$= a^2{x}^2-2abxy + b^2{y}^2 (Ans.)$

$x^3+xy$এর বর্গ $=(x^3+xy{)}^2$

$=(x^3{)}^2+2x^{3}xy+(xy{)}^2$

$=x^6+2x^{4}y+x^2{y}^2$ (Ans.)

11a - 12b এর বর্গ $=(11a-12b{)}^2$

$=(11a{)}^2-2\times 11a\times 12b+(12b{)}^2$

$=121a^2-264ab+144b^2$ (Ans.)

$6x^{2}y – 5x{y}^2$ এর বর্গ $=(6x^{2}y-5x{y}^2{)}^2$

$=(6x^2\times y{)}^2-2\times 6x^2\times y\times 5x{y}^2+(5x{y}^2{)}^2$

$= 36x^4{y}^2 - 60x^3{y}^2+ 25x^{2}y$ (Ans.)

x - y এর বর্গ = = (x - y)² = {-1 (x + y)}²

=(-1)² (x + y)² = (x + y)² = x² + 2xy + y² (Ans.)

-xyz - abc এর বর্গ = (-xyz - abc)²

= {-1(xyz + abc)}² = (-1)² (xyz + abc)²

= (xyz + abc)² = (xyz)² + 2xyz x abc + (abc)²

= x²y²z² + 2abcxyz + a²b²c² (Ans.)

$a^2{x}^3-b^2{y}^4$ এর বর্গ $=(a^2{x}^3-b^2{y}^4{)}^2$

$=(a^2{x}^3{)}^2-2a^2{x}^3{b}^2{y}^4+(b^2{y}^4{)}^2$

$=a^4{x}^6-2a^2{b}^2{x}^3{y}^4+b^4{y}^8$ (Ans.)

108 এর বর্গ $=(108{)}^2=(100+8{)}^2$

$=(100{)}^2+2\times 100\times 8+(8{)}^2$

= 10000 + 1600 + 64

= 11664 (Ans.)

606 এর বর্গ $=(606{)}^2=(600+6{)}^2$

$=(600{)}^2+2\times 600\times 6+(6{)}^2$

= 36000 + 7200 + 36

= 367236 (Ans.)

a - b + c এর বর্গ$=(a-b+c{)}^2$

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

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

$= a^2+ b^2+c^2-2ab - 2bc + 2ca\mathbf{ }\mathbf{(}\mathit{A}\mathit{n}\mathit{s}\mathbf{.}\mathbf{)}$

আমরা জানি,

$(p+q+r{)}^2=p^2+q^2+r^2+2pq+2qr+2pr$

এখানে, p = ax, q = b এবং r = 2 ধরে,

$(ax+b+2{)}^2=(ax{)}^2+(b{)}^2+(2{)}^2+2\times \left(ax\right)\times b+2\times \left(b\right)\times \left(2\right)+2\times \left(ax\right)\times \left(2\right)$

$=a^2+b^2+4+2abx+4b+4ax$ (Ans.)

আমরা জানি,

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

এখানে, a = xy, b = yz এবং c = – zx ধরে

$(xy+yz-zx{)}^2=(xy{)}^2+(yz{)}^2+(-zx{)}^2+2(\times xy)\times \left(yz\right)+2\times \left(yz\right) \times (-zx) + 2\times (-zx)\times \left(xy\right)$

$= x^2{y}^2 + y^2{z}^2 +z^2{x}^2+2xyz-2xy{z}^2-2x^{2}yz$ (Ańs.)

আমরা জানি,

$(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ac$

এখানে, a = 3p, b = 2q এবং c = - 5r ধরে,

$(3p+2q-Sr{)}^2=(3p{)}^2+(2q{)}^2+(-5r{)}^2+2\times \left(3p\right)\times \left(2q\right)+2 \times \left(2q\right)\times (-5r) + 2\times \left(3p\right)\times (-5r)$

$=9p^2+4q^2+25r^2+12pq-20qr-30pr$ (Ans.)

আমরা জানি,

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

এখানে, $a=x^2, b=-y^2$ এবং $c=(-z^2)$ ধরে

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

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

আমরা জানি,

$(x+y+z{)}^2=x^2+y^2+z^2+2xy+2yz+2zx$

এখানে, $x=7a^2,y=8b^2$ এবং $z=-5c^2$ ধরে

$(7a^2+8b^2-5c^2{)}^2=(7a^2{)}^2+(8b^2{)}^2+(-5c^2{)}^2+2\times \left(7a^2\right)\times \left(8b^2\right)+2\times \left(8b^2\right)\times (-5c^2)+2\times (-5c^2)\times \left(7a^2\right)$

$=49a^4+64b^4+25c^4+112a^2{b}^2-80b^2{c}^2-70c^2{a}^2$