Question:সৃত্রের সাহায্যে নিচের রাশিগুলোর বর্গ নির্ণয় কর। (ক). 5a + 7b (খ). 6a + 3 (গ). 7p - 2q (ঘ). ax - by ( ঙ). `x^3 + xy` (চ). 11a - 12b (ছ). `6x^2y - 5xy^2` ( জ).` - x - y` (ঝ).` - xyz - abc` (ঞ). `a^2x^3` (ট).` 108` (ঠ). `606` (ড).` 597` (ঢ).` a - b + c` (ণ). ax + b + 2 (ত).` xy + yz - zx` (থ).` 3p + 2q - 5r ` (দ). `x^2 - y^2 - z^2` (ধ). `7a^2 + 8b^2 - 5c^2`
Answer ক.`= (5a)^2 + 2.5a.7b + (7b)^2` `= 25a^2 + 70ab + 49b^2` উত্তর`: 25a^2 + 70ab + 49b^2` খ. `(6x + 3)^2` `= (6x)^2 + 2. 6x. 3 + 3^2` উত্তর: `= 36x^ + 36x + 9` গ. `(7p - 2q)^2` `= (7p)^2 - 2. 7b. 2q + (2q)^2` `= 49p^2 - 28pq + 4q^2` উত্তর`= 49p^2 - 28pq + 4q^2` ঘ. `(ax - by)^2` `= (ax)^2 - 2.ax.by + (by)^2` `= a^2x^2 - 2abxy + b^2y^2` উত্তর: `a^2x^2 - 2abxy + b^2y^2` ঙ. `(x^3 + xy)^2` `= (x^3)^2 + 2.x^3.xy + (xy)^2` `= x^6 + 2x^4y + x^2y^2` উত্তর: `x^6 + 2x^4y + x^2y^2` চ. `(11a - 12b)^2` `= (11a)^2 - 2. 11a. 12b + (12b)^2` `= 121a^2 - 264ab + 144b^2` উত্তর: `121a^2 - 264ab + 144b^2` ছ. `(6x^2y - 5xy^2)^2` `= (6x^2y)^2 - 2.6x^2y. 5xy^2 + (5xy^2)^2` `= 36x^4y^2 - 60x^3y^3 + 25x^2y^4` উত্তর: `36x^4y^2 - 60x^3y^3 + 25x^2y^4` জ. `(- x - y)^2 = {- (x + y)}^2` `= (x + y)^2` `= x^2 + 2xy + y^2` উত্তর: `x^2 + 2xy + y^2` জ. `(- xyz - abc)^2` `= {- (xyz + abc)}^2` `= (xyz + abc)^2` `= (xyz)^2 + 2.xyz.abc + (abc)^2` উত্তর: `= x^2y^2z^2 + 2abcxyz + a^2b^2c^2` ঞ. `(a^2x^3 - b^2y^4)^2` `= (a^2x^3)^2 - 2.a^2x^3. b^2y^4 + (b^2y^4)^2` `= a^4x^6 - 2a^2b^2x^3y^4 + b^4y^8` উত্তর `: a^4x^6 - 2a^2b^2x^3y^4 + b^4y^8` ট. `(108)^2 = (100 + 8)^2` `= (100)^2 + 2.100. 8 + (8)^2` `= 10000 + 1600 + 64` `= 11664` উত্তর `: 11664` ঠ. `(606)^2 = (600 + 6)^2` `= (600)^2 + 2. 600. 6 + 6^2` `= 360000 + 7200 + 36` ` = 3672236` উত্তর `: 367236` ড. `(597)^2 = (600 - 3)^2` `= (600)^2 - 2. 600. 3 + 3^2` `= 360000 - 3600 + 9` `= 356409` উত্তর : 356409 ঢ. `(a - b + c)^2` `= {a - (b - c)}^2` `= a^2 - 2.a(b - c) + (b - c)^2` `= a^2 - 2a(b - c) + b^2 - 2bc + c^2` `= a^2 - 2ab + 2ac + b^2 - 2bc + c^2` `= a^2 + b^2 + c^2 - 2ab - 2bc + 2ca` উত্তর: `a^2 + b^2 + c^2 - 2ab - 2bc + 2ca` ণ. `(ax + b + 2)^2` `= {ax + (b + 2)}^2` `= (ax)^2 + 2.ax (b + 2) + (b + 2)^2` ` = a^2x^2 + 2ax (b + 2) + b^2 + 2. b. 2 + 2^2` `= a^2x^2 + 2abx + 4ax + b^2 + 4b + 4` উত্তর `: a^2x^2 + 2abx + 4ax + b^2 + 4b + 4` ত. `(xy + yz - zx)^2` `= {xy + (yz - zx)}^2` `= (xy)^2 + 2.xy. (yz - zx) + (yz - zx)^2` `= x^2y^2 + 2xy (yz - zx) + (yz)^2 - 2.yz.zx + (zx)^2` `= x^2y^2 + 2xy^2z - 2x^2yz + y^2z^2 - 2xyz^2 + z^2x^2` `= x^2y^2 + y^2z^2 + z^2x^2 - 2x^2yz + 2xy^2z - 2xyz^2` উত্তর `: x^2y^2 + y^2z^2 + z^2x^2 - 2x^2yz + 2xy^2z - 2xyz^2` থ. `(3p + 2q - 5r)^2` `= {3p + (2q - 5r)}^2` `= (3p)^2 + 2.3p (2q - 5r) + (2q - 5r)^2` `= 9p^2 + 6p (2q - 5r) + (2q)^2 - 2. 2q. 5r + (5r)^2` `= 9p^2 + 12pq - 30rp + 4q^2 - 20qr + 25r^2` `= 9p^2 + 4q^2 + 25r^2 + 12pq - 20qr - 30rp` উত্তর: ` 9p^2 + 4q^2 + 25r^2 + 12pq - 20qr - 30rp` দ. `(x^2 - y^2 - z^2)^` `= {x^2 - (y^2 + z^2)}^2` `= (x^2)^2 - 2. x^2. (y^2 + z^2) + (y^2 + z^2)^2` `= x^4 - 2x^2 (y^2 + z^2) + (y)^2 + 2. y^2. z^2 + (z^2)^2` `= x^4 - 2x^2y^2 - 2z^2x^2 + y^4 + 2y^2z^2 + z^4` `= x^4 + y^4 + z^4 - 2x^2y^2 + 2y^z^2 - 2z^2x^2` উত্তর: `x^4 + y^4 + z^4 - 2x^2y^2 + 2y^z^2 - 2z^2x^2` ধ. `(7a^2 + 8b^2 - 5c^2)^2` `= {7a^2 + (8b^2 - 5c^2)}^2 ` `= (7a^2)^2 + 2.7a^2. (8b^2 - 5c^2) + (8b^2 - 5c^2)^2` `= 49a^4 + 14a^2 (8b^2 - 5c^2) + (8b^2)^2 - 2. 8b^2. 5c^2 + (5c^2)^` `= 49a^4 + 112a^2b^2 - 70a^2c^2 + 6ab^4 - 80b^2c^2 + 25c^4` `= 49a^4 + 64b^4 + 25c^4 + 112a^2b^2 - 80b^2c^2 - 70c^2a^2` `= 49a^4 + 64b^4 + 25c^4 + 112a^2b^2 - 80b^2c^2 - 70c^2a^2`
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shitrer shahajje nicher rashigulor borog nirony karo. (k). 5a + 7b (kh). 6a + 3 (g). 7p - 2q (gh). ax - by ( ঙ). `x^3 + xy` (ch). 11a - 12b (cho). `6x^2y - 5xy^2` ( ja).` - x - y` (ঝ).` - xyz - abc` (ঞ). `a^2x^3` (t).` 108` (th). `606` (ড).` 597` (ঢ).` a - b + c` (n). ax + b + 2 (t).` xy + yz - zx` (tho).` 3p + 2q - 5r ` (do). `x^2 - y^2 - z^2` (dh). `7a^2 + 8b^2 - 5c^2`