Question:সূত্রের সাহায্যে গুণফল নির্ণয় কর: ক. `(a^2 + b^2) (a^4 - a^2b^2 + b^4)` খ. `(ax - by) (a^2x^2 + abxy + b^2y^2)` গ. `(2ab^2 - 1) (4a^2b^4 + 2ab^2 + 1)` ঘ. `(x^2 + a) (x^4 - ax^2 + a^2)` ঙ. `(7a + 4b) (49a^2 - 28ab + 16b^2)` চ. `(2a - 1) (4a^2 + 2a + 1) (8a^3 + 1)` ছ. `(x + a) (x^2 - ax + a^2) (x - a) (x^2 + ax + a^2)` জ.` (5a + 3b) (25a^2 - 15ab + 9b^2) (125a^2 - 27b^3)`
Answer ক. `(a^2 + b^2) (a^4 - a^2b^2 + b^4)` `= (a^2 + b^2) {(a^2)^2 - a^2. b^2 + (b^2)^2}` `= (a^2)^3 + (b^2)^3` `= a^6 + b^6` :. নির্ণেয় গুণফল =` a^6 + b^6` উত্তর: ` a^6 + b^6` খ. `(ax - by) (a^2x^2 + abxy + b^2y^2)` `= (ax - by) {(ax)^2 + ax. by + (by)^2}` `= (ax)^3 - (by)^3` `= a^3x^3 - b^3y^3` :. নির্ণেয় গুণফল `= a^3x^3 - b^3y^3` উত্তর : `a^3x^3 - b^3y^3` গ. `(2ab^2 - 1) (4a^2b^4 + 2ab^2 + 1)` `= (2ab^2 - 1) {(2ab^2)^2 + 2ab^2 .1 + 1^2}` `= (2ab^2)^3 - 1^3` `= 8a^3b^6 - 1` :. নিণেয় গুণফল `= 8a^3b^6 - 1` উত্তর: `8a^3b^6 - 1` ঘ. `(x^2 + a) (x^4 - ax^2 + a^2)` `= (x^2 + a) {(x^2)^2 - x^2. a + a^2}` `= (x^2)^3 + a^3` `= x^6 + a^3` :. নির্ণেয় গুণফল `= x^6 + a^3` উত্তর :`x^6 + a^3` ঙ. `(7a + 4b) (49a^2 - 28ab + 16b^2)` `= (7a + 4b) {(7a)^2 -7a. 4b + (4b)^2}` `= (7a)^3 + (4b)^3` `= 343a^3 + 64b^3` :. নির্ণেয় গুণফল `= 343a^3 + 64b^3` উত্তর:`343a^3 + 64b^3` চ. `(2a - 1) (4a^2 + 2a + 1) (8a^3 + 1)` `= (2a - 1) {(2a)^2 + 2a. 1 + 1^2} (8a^3 + 1)` `= {(2a)^3 - 1^3} (8a^3 + 1)` `= (8a^3 - 1) (8a^3 + 1)` `= (8a^3)^2 - 1^2` = `64a^6 - 1` :. নির্ণেয় গুণফল = `64a^6 - 1` উত্তর: `64a^6 - 1` ছ. `(x + a) (x^2 - ax + a^2) (x - a) (x^2 + ax + a^2)` `= (x^3 + a^3) (x^3 - a^3)` `= (x^3)^2 - (a^3)^2` =` x^6 - a^6` :. নির্ণেয় গুণফল =` x^6 - a^6` উত্তর: ` x^6 - a^6` জ.` (5a + 3b) (25a^2 - 15ab + 9b^2) (125a^2 - 27b^3)` `= (5a + 3b) {(5a)^2 - 5a. 3b + (3b)^2} (125a^3 - 27b^3)` `= {(5a)^3 + (3b)^3} (125a^3 - 27b^3)` `= (125a^3 + 27b^3) (125a^3 - 27b^3)` `= (125a^3)^2 - (27b^3)^2` `= 15625a^6 - 729b^6` :. নির্ণেয় গুণফল `= 15625a^6 - 729b^6` উত্তর: `15625a^6 - 729b^6`
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shoূtrer shahajje gunphol nirony karo: ka. `(a^2 + b^2) (a^4 - a^2b^2 + b^4)` kh. `(ax - by) (a^2x^2 + abxy + b^2y^2)` ga. `(2ab^2 - 1) (4a^2b^4 + 2ab^2 + 1)` gh. `(x^2 + a) (x^4 - ax^2 + a^2)` ঙ. `(7a + 4b) (49a^2 - 28ab + 16b^2)` ch. `(2a - 1) (4a^2 + 2a + 1) (8a^3 + 1)` cho. `(x + a) (x^2 - ax + a^2) (x - a) (x^2 + ax + a^2)` ja.` (5a + 3b) (25a^2 - 15ab + 9b^2) (125a^2 - 27b^3)`