Question:সূত্রের সাহায্যে নিচের রাশিগুলোর ঘন নির্ণয় কর: ১. ক.3x + y খ. `x^2 + y` গ. 5p + 2q ঘ. `a^2b + o^2d` ঙ. 6p - 7 চ. ax - by ছ. `2p^2 - 3r^2` জ. `x^3 + 2` ঝ. 2m + 3n - 5p ঞ. `x^2 - y^2 + z^2` ট. `a^2b^2 - c^2d^2` ঠ. `a^2b - b^3c` ড. `x^3 - 2y^3` ঢ. 11a - 12b ণ.` x^3 + y^3`
Answer ক. `(3x + y)^3` `= (3x)^3 + 3.(3x)^2. y + 3.3x.y^2 + y^3` `= 27x^3 + 27x^2y + 9xy^2 + y^3` উত্তর: `27x^3 + 27x^2y + 9xy^2 + y^3`ু খ. `(x^2 + y)^3` `= (x^2)^3 + 3.(x^2)^2. y + 3.x^2. y^2 + y^3` `= x^6 + 3x^4y + 3x^2y^2 + y^3` উত্তর:` x^6 + 3x^4y + 3x^2y^2 + y^3` গ. `(5p + 2q)^3` `= (5p)^3 + 3.(5p)^2. 2q + 3. 5p.(2q)^2 + (2q)^3` `= 125p^3 + 150p^2q + 60pq^2 + 8q^3` উত্তর: `125p^3 + 150p^2q + 60pq^2 + 8q^3` ঘ. `(a^2b + o^2d)^3` `= (a^2b)^3 + 3.(a^2b)^2. c^2d + 3. a^2b.(c^2d)^2 + (c^2d)^3` `= a^6b^3 + 3a^4b^2.c^2d + 3a^2b.c^4d^2 + c^6d^3` `= a^6b^3 + 3a^4b^2c^2d + 3a^2bc^4d^2 + c^6d^3` উত্তর: `a^6b^3 + 3a^4b^2c^2d + 3a^2bc^4d^2 + c^6d^3` ঙ. `(6p - 7)^3` `= (6p)^3 - 3.(6p)^2. 7 + 3.6p.7^2 - 7^3` `= 216p^3 - 3.36p^2. 7 + 3.6p.49 - 343` `= 216p^3 - 75p^2 + 882p - 343` উত্তর: `216p^3 - 75p^2 + 882p - 343` চ. `(ax - by)^3` `= (ax)^3 - 3.(ax)^2. by + 3. ax.(by)^2 - (by)^3` `= a^3x^3 - 3.a^2x^2. by + 3. ax. b^2 y^2 - b^3 y^3` `= a^3x^3 - 3.a^2bx^2y + 3ab^2xy^2 - b^3y^3` উত্তর: `a^3x^3 - 3.a^2bx^2y + 3ab^2xy^2 - b^3y^3` ছ. `(2p^2 - 3r^2)^3` `= (2p^2)^3 - 3(2p^2)^2. 3r^2 + 3. 2p^2.(3r^2)^2 - (3r^2)^3` `= 8p^6 - 3. 4p^4. 3r^2 + 3. 2p^2. 9r^4 - 27r^6` `= 8p^6 - 36p^4r^2 + 54p^2r^4 - 27r^6` উত্তর: ` 8p^6 - 36p^4r^2 + 54p^2r^4 - 27r^6` জ. `(x^3 + 2)^3` `= (x^3)^3 + 3.(x^3)^2. 2 + 3.x^3. 2^2 + 2^3` `= x^9 + 3.x^6. 2 + 3.x^3. 4 + 8` `= x^9 + 6x^6 + 12x^3 + 8` উত্তর: `x^9 + 6x^6 + 12x^3 + 8` ঝ. `(2m + 3n - 5p)^3` `= {2m + (3n - 5p)}^3` `= (2m)^3 + 3. (2m)^2. (3n - 5p) + 3. 2m. (3n - 5p)^2 + (3n - 5p)^3` `= 8m^3 + 12m^2 (3n - 5p) + 6m (9n^2 - 30np + 25p^2) + 27n^3 ` `- 3.9n^2. 5p + 3. 3n. 25p^2 - 12p^3` `= 8m^3 + 36m^2n - 60m^2p + 54mn^2 - 180mnp + 150mp^2 ` `+ 27n^3 - 135pn^2 + 225np^2 - 125p^2` `= 8m^3 + 27n^3 - 125p^3 + 36m^2n - 60m^2p + 54mn^2 - 135 pn^2` ` + 150mp^2 + 225np^2 - 180mnp` উত্তর: ` 8m^3 + 27n^3 - 125p^3 + 36m^2n - 60m^2p + 54mn^2 - 135 pn^2 ` `+ 150mp^2 + 225np^2 - 180mnp` ঞ. `(x^2 - y^2 + z^2)^3` `= {(x^2 - y^2) + z^2}^3` `= (x^2 - y^2)^3 + 3. (x^2 - y^2). z^2 + 3. (x^2 - y^2) (z^2)^2 + (z^2)^3` `= (x^2)^3 - 3. (x^2)^2 .y^2 + 3. x^2. (y^2)^2 - (y^2)^3 + 3{(x^2)^2 ` `- 2. x^2. y^2 + (y^2)^2}. z^2 + 3x^2z^4 - 3y^2z^4 + z^6` `= x^6 - 3x^4y^2 + 3x^2y^4 - y^6 + 3z^2x^4 - 6x^2y^2z^2 ` `+ 3y^4z^2 + 3z^4x^2 - 3y^2x^4 + z^6` উত্তর: `x^6 - 3x^4y^2 + 3x^2y^4 - y^6 + 3z^2x^4 - 6x^2y^2z^2 ` `+ 3y^4z^2 + 3z^4x^2 - 3y^2x^4 + z^6` ট. `(a^2b^2 - c^2d^2)^3` `= (a^2b^2)^3 - 3.(a^2b^2)^2. c^2d^2 + 3. a^2b^2. (c^2d^2)^2 - (c^2 d^2)^3` `= a^6b^6 - 3a^4b^4c^2d^2 + 3a^2b^2c^4d^4 - c^6d^6` উত্তর: `a^6b^6 - 3a^4b^4c^2d^2 + 3a^2b^2c^4d^4 - c^6d^6` ঠ. `(a^2b - b^3c)^3` `= (a^2b)^3 - 3. (a^2b)^2. b^3c + 3. a^2b. (b^3c^2) - (b^3c)^3` `= a^6b^3 - 3a^4b^2.b^3c + 3a^2b. b^6c^2 - b^9c^3` `= a^6b^3 - 3a^4b^5c + 3a^2b^7c^2 - b^9c^3` উত্তর: `a^6b^3 - 3a^4b^5c + 3a^2b^7c^2 - b^9c^3` ড. `(x^3 - 2y^3)^3` `= (x^3)^3 - 3.(x^3)^2 . 2y^3 + 3. x^3. (2y^3)^2 - (2y^3)^3` `= x^9 - 6x^6y^3 + 12x^3y^6 - 8y^9` উত্তর: `x^9 - 6x^6y^3 + 12x^3y^6 - 8y^9` ঢ. `(11a - 12b)^3` `= (11a)^3 - 3. (11a)^2 . 12b + 3.11a. (12b)^2 - (12b)^3` `= 1331a^3 - 4356a^2b + 4752ab^2 - 178b^3` উত্তর: `1331a^3 - 4356a^2b + 4752ab^2 - 178b^3` ণ.` (x^3 + y^3)^3` `= (x^3)^3 + 3. (x^3)^2 . y^3 + 3.x^3. (y^3)^2 + (y^3)^3` `= x^9 + 3x^6y^3 + 3x^3y^6 + y^9` উত্তর: `x^9 + 3x^6y^3 + 3x^3y^6 + y^9`
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shoূtrer shahajje nicher rashigulor ghn nirony karo: ১. ka.3x + y kh. `x^2 + y` ga. 5p + 2q gh. `a^2b + o^2d` ঙ. 6p - 7 ch. ax - by cho. `2p^2 - 3r^2` ja. `x^3 + 2` ঝ. 2m + 3n - 5p ঞ. `x^2 - y^2 + z^2` t. `a^2b^2 - c^2d^2` th. `a^2b - b^3c` ড. `x^3 - 2y^3` ঢ. 11a - 12b n.` x^3 + y^3`