Factorise: 14x6 – 45x3y3 – 14y6

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Sudha Swaminathan

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(2X^3 - 7Y^3) (7X^3+2Y^3)
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(7x3+2y3)(2x3-7y3)
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(7y3 + 2y3) (2x3 - 7y3)
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Let us put x3 = a and y3 = b so that 14x6 -- 45x3y3 -- 14y6 = 14a2 -- 45ab -- 14b2 = 14a2 -- 49ab + 4ab -- 14b2 = (2a -- 7b) (7a + 2b) ⇒ 14x6 -- 45x3y3 -- 14y6 = (2x3 -- 7y3) (7x3 + 2y3)
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=14x^6-49x^3y^3+4x^3y^3-14y^3 =7x^3(2x^3-7y^3)+2y^3(2x^3-7y^3) =(2x^3-7y^3) (7x^3+2y^3)
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(2X^3-7Y^3)(7X^3+2Y^3)
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14x6 - 45x3y3-14y6 = 14x6-49x3y3+4x3y3-14y6 = 7x3 (2x3-7y3)+2y3(2x3-7y3) = (7x3+2y3)(2x3-7y3)
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